TL:DR; I never felt sexy, but now I do and I know a lot of guys have trouble with this. In my case my upbringing was a major cause and coming to terms with it helped me a lot.
This question hits a sensitive spot. I'm a young guy and I've been feeling unsexy pretty much all my life. It's only lately I can view myself in a sexy, desirable light. And it hurts my very bones to see how many guys cannot, how many guys suffer in silence without even knowing what they truly are.
I was raised by a misandristic mother. I didn't even realize this until I was like 20 years old, and even then the extent of the damage she'd done took a few more years to sink in and become fixable.
Basically she taught me that guys are bad, guys rape, guys bother girls, if the world would be run by women it would be a better place. Guys take all the leading spots, guys oppress women who just want a piece of the cake. Etcetera, etcetera.
Some of these things she said outright. Others, she implied. I exaggerate a little - she wasn't exactly openly hateful - but the message was there and it was clear.
She treated my dad like shit, basically crushing his sense of self-worth and agency over the years. She turned us young, impressionable kids against him by using her position as the family's martyr to blame him for all her hardships. Anything he did (or didn't do) was deemed sub-par, until all he did was go to work and sleep in front of soccer on the TV. Even then, she'd drone on about how sport was a man's silly game and that it's pointless to watch. My dad wasn't exactly a saint but he did not deserve what he got.
These things in concerto culminated in me a sort of subtle, deep-rooted sense of being wrong because I'm a man. In elementary school, around that age when guys would start pursuing girls in one way or another, I would sit back and watch in disgust. I would pride myself on being one of the good guys who didn't bother girls and just admired them from a distance. I didn't get involved.
As you can probably see easily, this led to a lot of troubles later in life. I couldn't talk to girls for shit. I put them on a pedestal. 'Not getting the girl' became a source of shame, a destructive internal conflict. I was supposed to be one of the good ones! My mom raised me to respect girls and hold them as the beautiful opposites of my male nature! If a girl likes me I'm the lucky one.
'Feeling sexy' was about as far from my reality as flying pigs. I'm a guy, right? I'm wrong. My kind is responsible for oppressing women, for raping children, for hurting the weak. My kind destroys life, while women create life. I have to fight my nature in order to be civilized. I have a disgusting hairy body. My over-sized feet smell and I have to wash my bedclothes every week or they'll smell like dirty man. Ugh.
I'm lucky in writing this today from a position of having pretty much worked my way through all of this shit. I understand how my mom's upbringing gave me a bias. I've banished it from my mind and today I do feel sexy, in fact I feel sexy as fuck and I understand what it means to be a sexual creature. I'm extremely happy with myself and I'm not afraid of my nature. I think about others in terms of people first, and male/female second. I have a healthy view on both sexes now.
I've tried forgiving my mom for all of this. I don't really blame her for the problems I've had - she was a product of her own upbringing and life experiences, and it doesn't much matter what she did or didn't do because it's in the past. Still, I haven't managed to completely absolve her because she still carries her misandry around. Just the other week we were watching a movie with the family and there was a short scene showing a girl getting pounded doggystyle by a guy. They finished and laid back together, shared a cigarette and a lot of smiles. I smiled too because sex is awesome, but mom just shook her head and looked disgusted.