A fantasy created in morbid circumstance...
Claire and Steve met during a rather harsh time. Here they both were, prisoners on a weird island, and then suddenly the island is attacked and polluted with zombies. Both, struggling to survive, ended up meeting each other and finding companionship, which makes perfectly good sense. After all, they were basically the only non-infected, non-crazy people alive on the island. Without each other, their lives would've ended long before they escape Rockfort Island.
In many ways, Steve is another version of Sherry. In a fan point of view, his first scene left fans forever hating him out of a first impression. He was fated for life. Claire seemed to automatically care about Miss Birkin, but seemed rather frustrated and annoyed with Steve. It wasn't until he saved her from the Bandersnatch that Claire lightened up, and even tricked him, which seemed like she was actually flirting at the same time.
Obviously, Steve had feelings for Claire since the beginning, although they were purely physical at the time. His feelings seemed to develop into a romantic form during the plane ride to the Antarctic. There, he leaned in for a kiss while Claire was sleeping. If Claire had not stirred in her sleep he most likely would have kissed her, no doubt awakened her as well. Claire, on the other hand, didn't think much of the guy due to his obnoxious attitude. He got in the way more than once, and slowed her down numerous times. He later apologizes for this, and Claire doesn't hold it against him. Claire's affection for Steve stems from when she realizes how lonely he is after his statement of guns being more dependable than people.
Steve expresses his feelings for Claire through words most of the time, but the player can tell Claire develops a liking for the boy due to her expressions. Almost after every cutscene she gives either a confused, affectionate, or concerned look. The most notable one is after Steve is shot by 'Alexia' in the Ashford Manor. Steve says it's just a scratch and runs off pretending it doesn't hurt. Claire makes an expression revealing frustration in the boy’s need to be strong about everything. She knows he's in emotional and physical pain, but refuses to be helped. In fact, the only time he opened up was when he revealed the truth about his father. And even then, all he wanted her to do is listen... because no one would before.
Steve eventually calms down with his flirting and only lets his true feelings out when Claire cannot notice. He leans in for a kiss as she sleeps and he stares at her while he's moving the car drill. Also, his need to protect her is almost as amazing as her need to protect Sherry. Of course, Claire wants to protect Steve as well, but the opportune moments hardly occur. Mr. Burnside saved Claire over five times on Rockfort, and other times in the Antarctic. He kills Alfred for Claire, and attempts the same with Nosferatu. His luck runs out there, as the monster's antenna knocks him off a platform, and it's up to Claire to save him this time. Steve is horrified with himself, even though he's done more than enough.
When Steve and Claire reunite after the boy is kidnapped by Alexia, he does not go out and say he's been injected by something. When Steve begins transforming Claire is absolutely devastated. She screams his name heartbreakingly and helplessly asks him to stop. The fact the player has to run from Steve instead of fight is another hint that Claire would never want to hurt him - monster or not.
Perhaps the most obvious and precious moment for the two is when Steve is about to decapitate Claire, seeing her as prey. He moans her name, still having a human-side to him. He risks his life, once again, for Miss Redfield... and dies because of it. His last sentence is his confession of love; his very last word is her name. He fell quickly, but passionately, in love because Claire was the only one who understood him.
For fans, there's a split opinion on Claire and Steve's relationship. Many people like it, many people don't. Although Steve's feelings are canon, S.D. Perry, who is known for being biased, chose not to acknowledge any of Claire's feelings for Steve. In the Code: Veronica comics, the artist/author obviously likes the pairing, as he made a point to add extra scenes where Claire herself was about to admit her attraction. Having different people work on different projects such as the comics, novels, etc. makes it hard for fans to pinpoint exactly what the characters may have been feeling.
Or Maybe Not...
It actually can be debated whether or not Claire returns feelings for Steve. It can even be debated if Steve sincerely loves Claire. Even though he plainly said so, it may have been due to him dying. Without making excuses, yes, Steve's feelings towards Claire are canon, but Claire's are subtext.
Steve's dead, yes, but Wesker made threats to bring him back, and with the unfinished story of Sherry, it's highly likely Steve will return with the blonde. And what then? Wesker's a manipulative man. He very well can persuade both that Claire is the 'bad one' - she abandoned Sherry, and if you want to dig deeper 'broke' her promise to escape with Steve (although that isn't exactly her fault). The scenario where Steve and Sherry remain on Wesker's side would be one of the best plot twists, considering both are extremely - extremely - unliked characters.
Even if Steve remains a good boy, he's no doubt infected with the T-Veronica. This fact would make it impossible for a relationship to work out between Claire and Steve. Claire's a good-hearted gal, but the virus running through Steve's veins probably doesn't interest her much.
It was doomed from the beginning, but there's still time.