Is it normal to fall deep in love and later deecide to be friends

I met wit a girl off a social media...I've fallen in love too quick till on the second time we met I had to beg for a kiss and she wasn't mean cuz she's in love wit me too. Told me a lot bout her ex and the terrifying shit he did to her...so I promised to love her like no other. But most often she'll remind me that she won't really fall in love wit a man like that anymore so I was like since that's the case we should jus be friends cuz if yu can't gimme the love I'm giving yu cuz of yur past then it aint no love.