There are 2 players. Each player tries to be the first saying "20" adding 1 or 2 to the number previously said by his opponent, then the other adds again 1 or 2 till on of them gets to 20.

How can I get a GTO solution for this game? Seems pretty easy but I'm missing something. Anyone knows?

Work backwards. On your last turn before choosing the count needs to be 18 or 19. To guarantee that it's 18 or 19, your previous choice has to add to 17. You can achieve this if the count before your turn is 15 or 16. In order for this to happen, the count after your choice on the previous turn has to be 14, you can achieve this if the count before your turn is 12 or 13. Keep working backwards.

desired count after your turn, going backwards:
20
17
14
11
8
5
2

If you go first, choose 2. If the other person goes first and chooses 2, and knows how to play, you should lose. If the other person chooses 1 then you choose 2 and go from there.

I could be totally wrong, but it seems right to me?

And although I suppose this could be classified as a GTO strategy, it's actually in a stricter class of solutions to games, which is to say, if you go first, you will always win. This differs from games like rock/paper/scissors where if you play a GTO strategy, you can not be beaten, but your only guarantee is to break even.

This is more like tic-tac-toe. If both players know the solution then there's no reason to play even one game. With roshambo and similar games, you can at least still gamble if both of you know the solution.

Such a perfect explanation, thx!!

This game is a version of Nim.
https://en.m.wikipedia.org/wiki/Nim

Rusty is correct. It is pretty easy to solve this game for any number and any number of choices at each point, for example first to say 1000 wins and one can add any number between 1-99 at each point. If you make the total 0 mod 100 you win.