The exact path lightning takes is going to generally be the one of least resistance, so if I follow your logic, you're thinking that by grounding it, you're lowering the resistance and thus increasing the likely-hood of a lightning strike.
I think the reality is, if lightning is going to hit your house, it is going to hit your house. By grounding your antenna, you're not going to divert a strike that would have otherwise gone to your neighbour's house, and likewise, the fact that they have a grounded antenna and you don't doesn't mean they're protecting you from a strike. Now, if it was a 300' antenna, that might be a different story, but on the scales we're talking about, I just don't see it.
Now what grounding it WILL do is make it more likely if your property does get hit, it will hit the antenna and follow the ground wire down to ground. Lightning is still looking for the best path to ground. If that happens to be by hitting your TV antenna, following it to the roof, going across some flashing on your roof to an attic-mounted fan, and then through your electrical wiring, that's how it will go. It could be down the side of a rain gutter, across the telephone wiring and down the utility pole. Point is, you are much better to have it go through the path you created than to have it find its own way.
Keep in mind, though for normal wiring/electrical purposes we would consider materials like asphalt shingles, wood, and plastic to be insulators, when you're talking about the 10 to hundreds of megavolts that lighting has, all those materials are conductive (metal is just a better conductor).
I think you're safer to have it grounded. Just be sure to install decent surge protection on the cables coming in (make sure the coaxial line from the antenna goes through a surge protector).
Frankly, it's a good idea to have surge protection on any sensitive electronics anyways. Even if lighting strikes your neighbour's house or a utility pole, there's a good chance you will at least have voltage spikes on your power/phone/etc lines that can damage anything plugged into them.