I think the reason might be because its not a set number. A GM doesn't think x number of moves every time. Some positions can be calculated rather quickly, with only a few moves ahead being required, and other positions really need deep calculation. So, the reality is that asking someone how many moves they can see ahead isn't really a fair question, unless you give them context. ie "How many moves ahead did you calculate in this position while you were playing?"
How come GM's dislike it when they are asked how many moves they can see ahead?

How many moves ahead can you see ? Surely even for an amateur it depends on the position, time control, shape etc.

I could see getting annoyed by the question. GMs, like many mortal players, can visualize an arbitrary number of moves ahead: no need to use a board at all. Once you realize that's possible -- as most people who ask don't -- it's kind of a dumb question.

The real question should not be the depth--because that can vary in each position.
The real question is, what are the many variations they actually consider in a position. Do they consider all sacrifices, every single time? Do they consider all pawn moves and piece moves even ones that don't look so great, or is their pattern recognition just so strong that they simply see a move and analyze that and see if their enemy has a good enough response?

Because it trivializes all the hard work and studying they have done. The question reflects someone who doesn't understand the intricacies of the game trying to define "greatness" by measuring a single, largely irrelivent point of data.
That's like saying Neil Armstrong wasn't a great astronaut because he's only been to the moon once.

Because the term "see X moves ahead" makes no sense. One can't calculate all the variations anyway. Thus sometimes one has to foresee a refutation on move 8 or even deeper. Sometimes (in quiet strategic positions & many endgames) there is no need for calculating deeply at all. One should think in terms of short-term plans.
Another issue is player's style. The classic example was a talk between Botvinnik and Tal. Tal has been sharing fantastic variations 10-move deep, while Botvinnik said: "You should exchange the knights, and leave the bishops on board".

Because it trivializes all the hard work and studying they have done. The question reflects someone who doesn't understand the intricacies of the game trying to define "greatness" by measuring a single, largely irrelivent point of data.
That's like saying Neil Armstrong wasn't a great astronaut because he's only been to the moon once.
I 100% agree with your first paragraph. But while GMs worked hard to get to where they are usually alone--Neil Armstrong's success is due to the thousands of aerospace, electrical, and even chemical engineers plus the rocket scientists that got him to the moon. Neil Armstrong is respected not because he's a great astronaut, but because he is a hero. He risked his life and trusted the very experimental devices that got him there. But still, I get your point, which is a good one.

IMCheap, obviously I am not asking if someone can see all possible combinations X moves deep at any random point of a Chess game. I am asking if someone can see X moves ahead as far as specific sequences of moves are concerned.
Think of the Sunday puzzle. It's easy; it requires that you visualize only one or two moves. But what about the more challenging puzzles where you are asked to mate in 7? Are you able to easily visualize the sequence of moves that will allow you to mate in 7?

I also love the exchanges between Tal and Botvinnik, but they really don't do justice the amount of calculation that Botvinnik would typically do.

IMCheap, obviously I am not asking if someone can see all possible combinations X moves deep at any random point of a Chess game. I am asking if someone can see X moves ahead as far as specific sequences of moves are concerned.
Think of the Sunday puzzle. It's easy; it requires that you visualize only one or two moves. But what about the more challenging puzzles where you are asked to mate in 7? Are you able to easily visualize the sequence of moves that will allow you to mate in 7?
That's why GMs hate this question. Obviously, "visualizing" is just playing blindfoldedly. I can easily visualize ANY number of moves ahead. But it does not mean that I will instantly see a mate in 7 or even 2. I may as well be looking at the wrong candidate moves.

People who ask this question don't really get it, so maybe you should show off and give a maximum answer. You know, in a pawn ending, when you're looking ahead 15-20 moves. Of course, they won't believe that you always look ahead that amount, but you can say "oh at least 5 moves, and as many as 15 or 20"! They don't even know the difference between moves and ply...

What is the difference between moves and ply (i.e. what is ply?)
White plays, then black plays - that's a move.
Only one side moves and that is a ply.

IMCheap, obviously I am not asking if someone can see all possible combinations X moves deep at any random point of a Chess game. I am asking if someone can see X moves ahead as far as specific sequences of moves are concerned.
Think of the Sunday puzzle. It's easy; it requires that you visualize only one or two moves. But what about the more challenging puzzles where you are asked to mate in 7? Are you able to easily visualize the sequence of moves that will allow you to mate in 7?
That's why GMs hate this question. Obviously, "visualizing" is just playing blindfoldedly. I can easily visualize ANY number of moves ahead. But it does not mean that I will instantly see a mate in 7 or even 2. I may as well be looking at the wrong candidate moves.
There you go. So the answer is: a nearly unlimited number of moves ahead. No need to overanalyze the question and try to find semantical errors.

What is the difference between moves and ply (i.e. what is ply?)
White plays, then black plays - that's a move.
Only one side moves and that is a ply.
Gotcha; thanks Diego, I'll be rooting for your boys at the World Cup!

Kraminik lost a game against Deep Fritz because he didn't see a Mate in 1!!
I guess most chess players can see several moves in a line, but sometimes even world champions don't see a mistake one move ahead.
The question of "how many moves you can see" makes more sense to chess softwares than to humans.
Some GM's like to say that Chess is not about seeing moves ahead, it's about finding the best next move, but I don't believe that's an entirely honest answer. Of course they need to calculate at least a few moves ahead, otherwise how can they tell which move is best? d4 might look like the best next move, but if playing d4 means that black will play exd4 and fork your knight and your bishop, then playing d4 is probably not the best move, and arriving at that conclusion requires that you think at least one move ahead.
Think about this: if a GM can play a Chess game with his eyes closed (most GM's can actually play more than one blindfold game at the same time) it's reasonable to conclude that they can draw in their minds an analysis board that they can use to see how certain combinations will play out. In that case, they can probably see dozens of moves ahead, but they like to say it's about finding the best next move, and seem annoyed when people ask them how many moves ahead they can see.