put an arrow in the white butterfly

[Asmodeus]

Or interact with it in any way?

[Zizi]

You can catch it if you are deft, by right clicking on it. It's not easy...

The white butterfly is a silk moth. They die soon after you catch them. Catch one of each gender and put them together in a nice big empty container and they produce eggs instead and then you are ready to start hunting feverishly for a mulberry tree so you can start your silk production industry.