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It doesn't follow because the conclusion has absolutely no relationship to the premise. Q isn't even involved in the premise. There not only is no logical reason, but no hint whatsoever in the premise that X and Y evolved from Q. Q just appears out of nowhere. Can you see that?

Q represents a common relationship based on similarities. Therefore it has logical significance as follows:
Prediction: If X and Y share certain calculated similarities in their genetic codes, then they are of common descent.
Test: Compare the genomes of X and Y for predicted similarities.
Conclusion: X and Y do share the calculated similarities, therefore they are of common descent.
Corollary: If X and Y share common descent, it follows that they have a common ancestor, Q.

Here is another fallacy I didnt' mention: The attributes of a part cannot be applied to the whole.

For this to be the case, the statement would have to be 'X has Z attributes. X and Y are both part of Q. Therefore Y has Z attributes'. That is not what the statement says.

Notice the first part of the logical premise by evolutionistis: X is SIMILAR to Y in Z. Similar is not the same as IDENTICAL, so the fallacy of equovication also applies. Humans and giraffes have the same number of neck vertabrae - should we assume we share a common ancestor with them?

If this is a fallacy of equivocation, then what word was misconstrued? If you are claiming it is the use of the word 'identical' where 'similar' is meant, then I challenge you to show where I used the word 'identical'. And if you are saying 'similar' was used when 'identical' was meant, then allow me to clarify: Wherever I said 'similar' I MEANT 'similar'.

As for the giraffe, no we should not assume common ancestry based solely on the evidence you cite. But making such a claim after taking all of the evidence available into account is another story.

Here's another important point: The evolutionist is assuming that the existence of similarity in designs or processes is evidence AGAINST design, when in fact this type of evidence is perfectly consistent with a designer.

Scientifically, evolutionists don't care in the least if there was a designer or not. That of course isn't to say that there are no evolutionists out there that use evolution as a club to bash religion. Just that they are overstepping the realm of science when they do so.