I don't think you can avoid the clump, with a garlic press. You can just toss it, though. Even Mustachians are allowed that much waste :-)
I've ended up just preferring the knife, too, like @GuitarStv . To me, cleaning a garlic press is maddening, whereas knives and cutting boards are easy. There's a bit of a knack to fine mincing, where you let the knife rock and rise under both hands...? Kind of hard to describe. I watched Julia Child do it on TV, at a young age, and was spellbound :-) When you get the hang of it you can get it as fine as you want in no time.
You do have to clean the stuff right away, in any case.
You don't have to waste the clump though. I save it in the freezer to pop in when I'm making broth, along with my veggie scrap and meat scraps bags =)
It's funny, I went the opposite direction. When I learned to truly cook from scratch, I was living in 500sqft, and I did *everything* with my knife. There just wasn't space to spare, not when my husband was working from home in that space and I was a full time student (stuff, stuff, stuff!) When we bought a house and had a lot more space, I got a garlic press for Christmas. I *love* it for quick dishes like oven roasted Brussel sprouts and so on. I also find it weird people have such a hard time cleaning it. Mine scrapes out really easily with my finger, or I'll blast water and it blows back the way it came. Mine came with a little tool with nubs for cleaning, but I never use it.
That being said, I think knowing how to do a true mince is a really valuable skill. And is a more potent garlic. The clump has a lot of the volatile "green" flavors of the garlic, so paste tends to be milder than fresh minced. For things like soup, where you want a potent garlic, mincing is the way to go. If it'll be baked instead of boiled though? Eh.