First of all, not being naturally aggressive and reacting to an opponent's attack is not necessarily a bad thing. Lots of fighters have built their careers on good counter-fighting skills, right? So, to begin with, a good idea is to polish your counterattacks. There are many good resources out there (books, DVDs etc) that you can choose from and study, depending on the style you practice.
On the other side, if you want to be proactive instead of reactive in your fighting, here's a few things you should consider:
1. An aggressive fighter must be able to depend on his conditioning. Are your body's energy systems able to cope with the needs of constantly moving forward and generating power? "Fatigue makes cowards of us all". If you want to be a hero, tons of sweat is part of the price you have to pay.
2. Having a plan always helps. It makes no sense if your aggression is only translated to charging your opponent like a bull. You must be aggressive in trying to force your game, so find out what your game is. For example, a fighter with Filipino Martial Arts experience might first try to angle and attack the moment his opponent tries to re-orient. The downside to having a plan is depending on it too much. Make sure you have a plan B in case plan A fails, otherwise you will keep on trying and failing which always results in frustration and a downward psychological spiral.
3. An aggressive fighter must be tough, i.e. able to take a strike and keep going until he overwhelms his opponent. Are you willing to take strikes and keep going? If not, once again, counter-fighting is your best option.
4. If you are not naturally aggressive, in order to have your chance on the offensive, you must first curb down your opponents aggression. This means that he must respect your power, always attacking must entail some fear factor for him. If every time he attacks, your counter-attack is a pat on his cheek, he'll keep on coming till he breaks you down. I repeat, I don't know which style of martial arts you practice, but keep in mind that beautiful, flowery techniques are useless if you can't back them up with power.
5. Finally, and this is the most important part, you must stop being judgmental about your game. This is not some sort of self-help BS, it's sports psychology. If every time you spar you're thinking "I'm not aggressive enough, I must attack more, oh, he's overwhelming me, I don't know what do do" and so on, your train of thoughts is on a downward slope. When fighting, your thoughts must NOT have either a qualitative or a quantitative dimension. Instead, focus on a set of simple, neutral set of instructions. For example, when an inexperienced fighter finds himself cornered, the first thing that happens is that his breathing is disrupted. Then, he just covers up, stops moving and practically turns himself into a punching bag. In this case he might focus on the set of instructions "breathe - keep moving - hit back" and repeat it over and over, in his mind, of course. Get your self a sparring partner and try the following drill (it is a DRILL, not all out fighting): have your partner throw continuous attacks at you (in combinations, not blitzkrieg). Your job is to block, evade and move away until you start to feel that you are loosing control, that you're overwhelmed and helpless. At exactly that moment, start repeating "breathe - keep moving - hit back" in your mind (or any other set of instructions you want to come up with) and unleash your counterattack till your opponent retreats. Now start throwing continuous attacks at him and have him block, evade, move out of the way until he feels overwhelmed. Continue this way back and forth, increasing the intensity if you wish. Try not to begin your counter-attack until you feel overwhelmed. This is a psychological exercise, the point of it being to taste frustration and still be able to spring into action, so you must get a little frustrated first! Give it a try and let me know the results.
Good luck with your training,
Filipino Kali Instructor
Systema Russian Martial Art Instructor
San Shou Coach