Insects often don't want to have me look directly at them. They seem to find comfort in hiding their eyes like a game of childhood peek-a-boo or hide-but-don't seek, where if they can't see you, it seems they hope you can't see them. I've had butterflies land on me and dragonflies too, but at first they will rotate so that I can't see their eyes. Usually, only after some trust has been established will they look directly at me. Once the trust is confirmed, as it will typically get with dragonflies, I'll have them cock their head in curiosity like a dog does, as they examine me and seem to try to get a beat on who I am.
Grasshoppers are especially cute about it. They will rotate around branches and back away and then when I find them, they hide some more sometimes rotating completely around a branch. What I've discovered, and few people know this, but it's a great photographer tip for insect photographers, is that almost all insects have a defense mechanism when feeling cornered where they drop off of whatever plant or structure they're on and free fall as far as they can. Often this lands them safely deep inside some plant or bush. Ladybugs are excellent at doing this. If you anticipate in advance, you can usually catch a ladybug and then gently put her on a flower to photograph.