Its easier to defend and wait for the other guy to make a mistake in grappling than it is to go on the offense. You see this in BJJ, judo, and wrestling, and I'd be amazed if it wasn't true in every other grappling art (sambo, shiao jiao, and the hundreds of national types of wrestling out there). Which is why all grappling sports I've heard of have some variation of stalling or defensive fighting penalties.
Really, you have to make a conscious effort to go onto the offense - it means failing a lot at first, being countered, being stuffed, being submitted. But you get better at it after awhile. It's not going to "just happen" one day - anyone who competes at high levels in any kind of grappling is going to tell you you have to consciously make a point of practicing offense.
Put it this way. Who cares if you win or lose while rolling in the club? The important part of club rolling (randori, scrimmaging etc) is to practice what you need to improve, not to win. Winning is only important in a competition or on the street.
Moreover, it doesn't matter if when you compete (or in self-defense) if you fight defensively or not, but it does matter if you fight defensively out of choice or because you have no other option. Ideally you should be able to switch between fighting defensively and offensively on a second's notice ... not going to happen if you aren't good at both.