Based on some common sense and on (not very numerous) articles online, I could think of the following advantages of roasting at home:
- you get the freshest possible coffee as you need it
- green beans are significantly cheaper than roasted ones, and keep longer
- you get finer control over the result (?) than just guided by labels on coffee bags
But there are also downsides:
- there's smoke during the roasting that you need to handle (see also Home roasting and ventilation)
- you need some specialized (and more or less expensive) equipment, or else invent tricks with a popcorn popper or a cast iron pan (which may not be too bad in fact)
- in order to obtain the finer control over the result you need to know what you're doing (which probably means you may not get a better-than-shop result in a number of initial trials) (e.g., this question)
All of that is my armchair coffee science though, and I hope that the practitioners here can say what of that is real and what is fictional, and what other reasons there are pro and contra homeroasting.