The One Direction singer allegedly pursued the 23-year-old music star after they split up for a first time last April when a picture of him kissing model Emma Ostilly appeared online.
Harry eventually ''wore her down'' and Taylor decided to give him a second chance late last year.
A source, who Taylor authorised to speak about her relationships on her behalf, told Vanity Fair magazine: ''He wore her down. He was all, like, 'You're amazing - I want to be with you. I want to do this.' ''
The 'Red' singer - who is rumoured to have written her hit 'I Knew You Were Trouble' about him after their initial separation - seemed very happy with the 1D hunk but she ended their romance in January after the blonde beauty felt he was always looking at ''every girl'' while they were a couple.
''The whole time she says she feels like he's looking at every girl,'' the source added, and when they were in London together the insider revealed he ''disappears one night and after that it was like he just didn't want to keep going''.
Taylor has had a number of failed relationships with famous men including Jake Gyllenhaal and John Mayer, and last year she had a ''two-month thing'' with Conor Kennedy, who was 17 at the time, and who the musician thought ''was awesome''.
Speaking about her exes, the source - who says Taylor has had age problems with all of her ex-boyfriends - explained: ''It was like a pendulum for her, swinging back and forth.
''She dated Jake and John when she was really young and they were in their 30s, and she got really hurt. So it was like, 'That hurt - this won't.' But then it did.''
While Taylor has reportedly had several romances with stars, she insists she has only ever dated ''exactly two people'' since 2010.
She explained: ''If you want some big revelation, since 2010 I have dated exactly two people, [Harry Styles and Conor Kennedy].''
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