These arguments seem unrelated. Any combination of opinions of the availability of abortions, the availability of euthanasia, and the availability of guns is possible. I'm not entirely sure who you're trying to strawman here (I'd say a generic liberal, except the liberals I've heard argue against gun ownership are way more upset about mass shootings than suicides).
Euthanasia is a choice you make governing your own life.
Abortion is a choice you make governing another being’s life.
As for suicide and guns - I’ve never heard this one before. There are plenty of options for suicide that don’t involve guns.