Quick Claw works such that it allows your Pokemon to move faster than your opponents if both your moves and the opponents moves belong to the same priority bracket.
Priority of course, refers to the order moves are executed, regardless of either Pokemon's Speed stat. For example, a Quick Attack used by a slower Pokemon will always be executed before a Tackle by a slower Pokemon. Protect has a priority of +3 so it almost always moves first, whereas Trick Room has -7, so it moves last. In Pokemon, the priority brackets range from -7 to +7.
If your Coalossal used a move with negative priority and the opponent used a move of 0, +1, +2, or above priority - you moved slower regardless. The same applies if you used a base 0 priority move and your opponent used a +1,+2, or above.
The only time you can say your game "glitched" (and something we can discuss if you remember what moves you and the opponent used that turn) is when neither of the above cases occured.