A pic's composition is right when it
looks right. There are no hard-and-fast rules (though when it
does look right, 9 times out of 10 it will conform to the so-called 'rule of thirds').
We learn the rules so that we'll be able to 'break' them by design... not just accident. There has to be a point. With people or animals, we naturally follow where they are looking, or moving towards, so we leave a little 'psychological space' in front of them.
The branches in this shot create a frame for the eagle. Personally, I like the bird being in the centre... maybe 'cos I'm accustomed to seeing the bald eagle as a symbol of the good 'ol US of A... and in its symbolic roles it's always dead centre. So it's both a handsome bird and a powerful symbol (actually, it's
so powerful that it's hard to see the bird without all that symbolism and mythology... a visual metaphor for America's perceived role in the world).
All this rambling is just to say that the pic looks very fine to me... and that composition is a personal thing.
I honestly don't think about composition when I'm shooting pix. But then, when I'm 'in the zone', I'm not thinking about much at all. I'm on 'auto-pilot', just reacting to what's going on around me. In these terms, composition is a 'feeling', not a set of rules...
Just my two-pennorth...