I'm going to go against the grain here and suggest something odd: Play his game. Just play it knowing there is a good chance you will lose at it, so that you don't get frustrated.
You have in front of you a guy who is very good defensively, and willing to be defensively. You're not used to that, as you're normally used to aggressive opponents, which I'm guessing means that you're used to being defensive. So you're aggressive skills are not that great. Note: none of this is guess work, it's what I got directly from your post.
By being aggressive against him, you may lose, but you will learn how to be aggressive. Since he's good at dealing with aggressive opponents (this part is guesswork, but I'm assuming that he spars the same people as you), you will have to work really hard at your aggressive fighting which, as long as you stay focused and fight calmly, can help you improve how you fight aggressively. Even if it's not your go-to fighting style, it's useful to be able to do, especially if in the future you're forced by situation or sparring partner to be aggressive.
Personally, I suck at being aggressive because most of the people I spar are either aggressive or less patient than me/less able to deal with my defensive footwork. It's something I'm working on, but I wish I had someone who was like the guy you described to spar regularly with.