When do you find yourself saying "here, kitty kitty" to a bobcat?

An encounter in California:

This past Saturday, I was mountain biking near the summit of Loma Alta, near Fairfax, when suddenly a big furry critter jumped off a berm crossing directly across the road in front of me. I got off my bike to get a closer look and there, staring me in the face about 20 feet in front of me, was a quite large bobcat. We kind of did a face-to-face stare down for a couple of minutes. Then it just laid down, and soon after, I sat down ... We sat there together for a good 20 minutes, perhaps even a half hour. Somewhat embarrassed to say, but 15 minutes into this viewing I actually uttered the words, "Here kitty-kitty!" What was I thinking! Eventually it stood up, gave a stretch and casually bounded down a stream-cut ravine.

How scary is a bobcat anyway? This isn't like saying "here, kitty kitty" to a tiger. (I'm thinking of the scene in "The Life of Pi" when Pi foolishly encourages the tiger to swim to the lifeboat.) A bobcat is double the size of a house cat. Me, I'm afraid of house cats roaming about outdoors. A double-size cat would scare me, but would it terrify me? Perhaps you've had a bobcat -- or other wild cat -- encounter you can tell us about.