Left-Handedness is a spectrum, from people who can only use their left hand.for everything, to people who only do a few things left-handed, but are naturally right handed for everything else. Then there are people like you, who can do some things lefty, some right, and some ambidextrous.

I am fully right-handed, except that I write with my left hand. I can't do anything else left-handed. I throw, swing a bat, play musical instruments, etc. all right handed. Yet, people see me writing, and say I'm left-handed. Even my mother, who should understand that I'm not really left-handed, tells people I'm a Lefty.

I'm right-handed. I just write left-handed, for some unfathomable reason. That does not make me left-handed.