Why is a robin hitting our bathroom window?

This is fairly common. A bird sees its reflection in a window, thinks the reflection is another bird in its territory, and attacks the reflection.

Last year I was throwing away a broken mirror. It was out in the yard waiting for my trip to the landfill. A bird spent hours every day attacking its own reflection in the mirror.

There is a reason we use the term "bird brain" to describe a not-too-bright person. Because birds are not always smart. 

The robin is seeing his reflection. He is attacking it. Put a clear film of contact paper (you can get it at the hardware store) over that window. The head-butting will stop. 

We had a bird keep hitting a specific window. It was by a bush but there was no nest. We thought it was because of the bird's reflection, it kept attacking itself or something. We eventually put an open umbrella in the bush as an easy way to keep it away. We left it there for a week with no more incidents and then took it away. No banging since but the bird might've just died.

I have not experienced this and have no idea why it is happening. Maybe it lives near your house and cannot see very well. But that is a wild guess.

Is there a mirror directly across.from the window. Or something inside.which is attractive to it.....

No, Marty, I haven't experienced a robin repeatedly flying into your window.