If a 5-set match went 6-3, 6-7, 3-6, 7-6, 6-3, then not counting the tiebreaker, 1 player would have served 28 games, the other 25. This is a different of 3 games, which would never happen as players have to alternate serve games. Why is the tiebreak considered a service game?
Tie breakers aren't considered serve games, they're neutral. But the alternating service pattern remains during and after a tie breaker.
No player is supposed to have an advantage in a tie breaker. To enforce this, players switch serve. One person serves once to start the tie breaker, and serve switches. From there on, they each serve twice and serve switches again till someone wins the game. This ensures the players have served the exact same number or just one off, which is the fairest solution.
The game after the tie breaker (first game of the next set), the service is switched again, so the player who served the last point of the breaker, now receives.
This keeps fairness of service switches, but can result in discrepancy of how many games a player has served.
There is nothing unfair about it. You cannot win the set by serving once more, you can only win a set by breaking your opponent (at least once more than he breaks you). So if player A serves first and is up 5-3 with one break, he has to serve once again and thus has to give player B a chance to re-break. This does not give him an advantage, as he is already one break up front and can only lose on this extra game.