People always want to be able to explain the things they are afraid of. It's human nature to want to know why something occurred, and many people will transpose their existing prejudices and views into the matrix of events, seize on something which supports their understanding, and go with that. In some cases, I daresay people pick the easy targets - after all, if you say it's about gun access, you run into a Second Amendment-toting wall; if you blame mental illness, you risk blaming a section of the community which needs help and understanding more than anything (and potentially draw attention to the lack of support provided for mental health services).
All in all - picking a target for blame is easy, self-affirming, possibly helps you to advance a political agenda, can be discarded for tomorrow's report, and sells copy. It's typically the ignorant who are the most certain about such things.
Getting into it in more depth...
Re: mental health - Mental health is frequently poorly-understood and poorly-supported, and I'm no expert on why that is or remains the case other than suggesting a general unease about the concept of something going wrong in a person's brain. It's sometimes hard to treat, it's often hard to deal with, and it's not like a physical injury where it can be viewed, assessed and checked, and there is little risk of any consequence to the people around the person in need of help. For many people, I suspect it's just too hard - and there's also the issue of demonising mental health issues, mental illness or psychiatric conditions if it's done without care.
Re: firearms - It'd be easy to blame particularly militant approach to the Second Amendment (without consideration of what the "right to bear arms" actually means in practice, particularly in suburban living and outside of a well-regulated militia) and the NRA. There may be some aspect of the American psyche, in some places, which equates firearms possession with independence and freedom. For whatever reason, there are lots of them, they are reasonably easy to obtain, they are probably the most effective force multiplier a single person can have, and it's political suicide even to suggest reducing access to weapons which no civilian could ever actually need. However, I don't see how the Second Amendment taken as a whole should protect an unfettered right to any and all firearms, and such an interpretation has (in my opinion) substantially contributed to the frequency and severity of mass killings with guns in the US.