Because neither one was able to admit to their true feelings their relationship started out in this way. Starting with "Go" Robin without any knowledge of who she was, nor any understanding of her language frees her from her bindings. Though she was cold to him in return; even after learning english by kissing him, it was mostly out of concern for his and Earth's safety, since at the time she was on the run from Gordanian slave drivers. After fighting them off with the rest of the newly formed team, they began to warm up to one and other. In "Sisters" Robin teaches Starfire many of earths customs, such as cotton candy and fireworks, whilst Starfire in return teaches Robin Tamaranian customs as well. Sometimes with disasterous results like in "Betrothed" when he along with the rest of the team were freaked out during the wedding feast Whether or not they admit it, they are more than willing to give their lives for each other. As proven in "Aftershock Part 1" When Starfire blocked an attack by Terra meant for Robin and when Robin fought Blackfire's guards to warn her of the sham wedding in "Betrothed."
As mentioned above, neither one ever consumated in their romantic feelings on the show. However those feelings were there from the beginning. It started with the kiss from "Go", at the time Robin didn't know about her ability to learn languages through lip contact. In "Date With Destiny" Starfire was insanely jealous when Robin was forced to date Killer Moth's daughter Kitten under threat of city destruction. Robin was equally jealous in "Betrothed" despite her arranged groom not being as appealing to her as she'd hope. Needless to say, despite their hesitense to admit so many of the other characters, have pointed out the obviousness of their romantic feelings such as in "Stranded" when Cyborg teases Robin about it. Robin of course denying it and in the process hurting Starfire's feelings. When Robin thought she misunderstood what he meant by "She's not my girlfriend." She fired back with the definition "A female with whom you have a pleasant and special association, including the sharing of enjoyable recreation, and occasionally the buying of bountiful floral arrangements." It was not until "Trouble In Tokyo" when they began to question their romantic relationship. When Robin first found out her ability to learn languages through lip contact, he was hurt at first because he now thought she only kissed him to learn English. A fact she now denies. However this didn't strengthen the romance, since Robin insists they are only heroes and nothing else. It wasn't until the end that he changed his mind and decided to pursue Starfire romantically and she in turn pursued him. Much like the beginning of their relationship, they started their future romance with a kiss.