Why do my Dragon Rushes sometimes result in no damage?

Solution 1:

A Dragon Rush is basically the throw of this game, and works similarly to other games. In Street Fighter for example, if you think your opponent will throw, you can hit throw as well and the throw will be 'teched', ending in both players in a neutral situation and no damage being taken.

The same concept can be applied to Dragon Rushes, except in FighterZ, you tech throws by pressing any attack button right as the Rush connects with you. This will cause the animation you describe where both characters clash blows, then pop up and away from each other, leaving you both in a neutral situation. It's worth noting that both players lose their air actions after a Rush tech - you can't airdash or double jump after the 'pop up'. It's a completely neutral situation.