I've always put my arms in the straps, and reached behind and did the clasps up ! Last year , I put my shoulder out, and the pain was horrific trying to get a bra on in my usual way, so I started buying stretch sports bras with no clasps at all.
The first one I tried, I couldn't get it over my head, I was in agony, it seemed far too small to go over my head and then struggle to get my arms through, with such a painful shoulder, and then I realised that I just needed to step into it, and pull it up, and it stretched and fitted without any problems.. it took the best part of the year for my shoulder to heal, but I'm sticking with the stretch sports bras now . No more fiddling with clasps !!