How important is it to fancy someones looks in a relationship?

Anonymous
So I have a boyfriend and we've been together for 2 years. He's very loving and things but recently he said that he's not interested in having sex anymore. Also while he's a sweet guy I don't really fancy him physically... he's altered since we first met.

Yesterday I was working with a guy and he was being really flirty with me. Like stroking my hands when I wasn't looking, and he said I was beautiful. And it made me get those butterflies you get at the start of a relationship and I realised that my boyfriend never really compliments me or flirts with me like that anymore.

As shallow as it sounds I really fancy this other guy and I don't know made me think about things. So my question is essentially: is it shallow of me to break up with someone who I don't fancy?
How important is it to fancy someones looks in a relationship?
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