That was John who did that. Peter ran slower, but went into the tomb.
The point could be - men need convincing, we are the weaker, so He uses us as priests. Those women, one of which was sinless, didn’t run during the WaY of the Cross and believed as soon as told - too strong for the priest role, they’re needed for initial evangelization/instruction while the men are cowering and using their testosterone and dumb strength/thick skin to feed the congregation and hear confessions.
Only one of us can carry and have the kid and mother-bear love like that - the other HAS to do SOMETHING special!