I don't know if this has been resolved yet, but if you have Cyber Phoenix on the field and you try and snatch your opponent's machine what happens? Can you not activate Snatch since it creates a loop or would CyberPhoenix be destroyed for causing a loop? I say the first, but the judge said the 2nd. But it's a toss up.

I dont know how the judge came up with phoenix being destroyed, but I think its either

A. Some sort of loop you cant purposely start

B. You get no monster from your opponent and snatch sits on the field (kinda like snatch against horus lvl 6, when horus lvl 6 is targeted)

It is Sheik's option A.

That judge is weird.

Actually I don't even believe it is a loop, if anything it is just like Call of the Haunted when you have Jinzo on the field. The spell looses its effect due to the monster effect but winds up sitting there meaninglessly. I say this because the card effect reads...
Which means that the loop would never happen and the card would sit there taking space in the owner's S/T zone. The only reason why this is relevant is because it is the difference between a wasted Snatch and nasty situation.

Or at least, that is how I read the effect.

Now, here's the question, the important part bolded for emphasis.

You did the bolding for Cyber Phoenix's text quite nicely. Combine that part with the part I bolded and we have ourselves a nice infinite loop.

You're right, it isn't difficult to figure out but, to be honest, your post doesn't really answer the question because it doesn't address the 'infinite loop' aspect.

If I target Cyber Dragon with Snatch Steal while I have Cyber Phoenix face up on the field, Cyber Dragon will switch to my side of the field. Once that happens Cyber Phoenix will recognize that Cy Dra is a face up machine on my side of the field and will negate anything that targets him.

This causes Snatch Steal to lose its effect while Cy Dra is on the same side of the field as Cy Phoenix, control will revert back to the previous controller.

This sequence of events will continue to repeat without end since none of these effects (once Snatch Steal resolves) use the chain so nothing can be chained to.

In other words, this is an infiite loop. According to the rules, if a player plays an effect that would cause an infinite loop, the game will revert back to the point before the effect activated and that player will not be allowed to play that effect.

Short Answer: You can't play Snatch Steal in this scenario.

I have to disagree with you here as I don't believe a loop would happen. Let us look at your scenario above.

Player A targets Player B's Cyber Dragon with Snatch Steal

Player B's Cyber Phoenix's secondary effect activates due to the trigger effect (a machine monster being targeted by a spell/trap) and negates Snatch Steal's effect.

So now we have a chain

Link 1 - Snatch Steal
Link 2 - Cyber Phoenix

We all know the ruling about chains and therefore know what will happen, but just in case someone is confused I will describe it below.

Link 2 activates negating the effect of Link 1
Link 1 resolves with no effect
Snatch Steal hits the field equipped to the Cyber Dragon with no effect.

To my knowledge this is how it would work out as the trigger effect would start a chain and negate Snatch Steal before it resolves. There would never be any switching of monsters due to the negation of Snatch's effect. Yet again, the only reason why I point this out is because there is a huge difference between a wasted Snatch and one in the hand.

If you pieced together everything properly, Magus and Tkwigit pretty much explained everything in full detail. There's really no argument. Remember the part of Cyber Phoenix's text that you bolded? There's no rule saying you can't target your opponent's machine type monsters. Your own Cyber Phoenix will not negate a card that targets your opponent's machine type monsters. A loop is created because once your opponent's machine type monster is brought to your side of the field, it will be considered yours, which will in turn trigger Cyber Phoenix's continuous effect, and negate Snatch Steal, which will return the machine type monster to your opponent. At this time, the machine type monster will no longer be influenced by Cyber Phoenix's continuous effect, so therefore, Snatch Steal's effect will be reinstated, bringing the machine type monster back to your side of the field. This will continue endlessly, therefore, the play is illegal.

To summarize:
The scenario being Player A's Cyber Phoenix and in-hand Snatch Steal VS Player B's Cyber Dragon.

1. Player A activates Snatch Steal, targeting Player B's Cyber Dragon. This is legal because Cyber Phoenix only prevents targeting of its controller's own Machine Type monster.
2. Player A's Snatch Steal resolves, bringing Player B's Cyber Dragon to Player A's side of the field. At the moment Cyber Dragon hits Player A's side of the field, Cyber Dragon is considered to be Player A's monster.
3. Player A's Cyber Phoenix's continuous effect is triggered, negating Snatch Steal's effect.
4. Cyber Dragon is returned to Player B's side of the field, Snatch Steal is still equipped.
5. Snatch Steal once again becomes active because Cyber Dragon is no longer considered Player A's monster (Cyber Dragon being on Player B's side of the field).
6. Cyber Dragon is brought over to Player's A's side of the field, ownership having shifted once again to Player A.

The infinite loop is established, and the game will return to the state before the infinite loop was achieved. The play that cause the infinite loop is considered illegal.

Did you think that Snatch Steal could somehow take a monster before fully resolving? Now is there anything you'd like to challenge? Like perhaps how Cyber Phoenix should be destroyed just for causing all this confusion?

I agree with Magnus. You shouldn't be able to activate Snatch since you are knowingly causing a loop. It won't just sit there meaninglessly once active.

Your arguement is based on the assumption that Cyber Phoenix has a triggered effect outside of its "draw 1 card" aspect, it does not.

This is directly from the FAQ:

As we all know, continuous effects never use the chain because they have no spell speed. Cards like Jinzo, Horus the Black Flame Dragon LV 6, Command Knight and similar cards have continuous effects much like Cyber Phoenix.

There are two very important ideas that you are understanding incorrectly in this portion of your post:

1 - You assume that Cyber Phoenix will negate the effect of Snatch Steal before it can resolve.

2 - Due to the previous point, you assume that control of the monster would not switch.

The effect of Cyber Phoenix does negate spell/trap effects that target machine monsters, but it will only do so for monster that are on your side of the field. If you target Cyber Dragon with Snatch Steal we can assume a few things:

1 - It's not on your side of the field

2 - It is outside of Cyber Phoenix's area of influence

By your logic, Cyber Phoenix would negate Snatch Steal before control could switch, but how could it? Cyber Phoenix only negates the effects of spell/traps that target a face up machine on YOUR side of the field. If control never switched, as you stated, it would be impossible for Snatch Steal to have been negated since Cyber Dragon never switched over to your side of the field.

Control MUST switch in order for Snatch Steal to be negated.

Snatch Steal, again, can not be activated in this scenario.

It is so hard to accept it :sleep:

Ah, you are correct as it seems I did misunderstand the card. Thanks for the clarification and that's why this is here, to help us understand the cards better.

Sorry for the bother.