I'm looking for a manga where the protagonist is put into situations that can be misconstrued as romantic, either by the reader, the protagonist themselves, and/or the others characters in the story.

Maybe the protagonist assumes that someone had romantic intentions towards them, act accordingly, only to figure out that they are very, very wrong. (The manga It's Not My Fault That I'm Not Popular! had some chapters like this.) Maybe neither are actually remotely interested in each other, even though it may appear to the readers or others in the story that this is the case.

I especially love it when the romantic subtext are deliberately left ambiguous. As in, are we making mountains out of molehills or is there actually something there? The best example I can think of that's like this is Natsume Yuujinchou. Because there are these moments like the way Natori invites Natsume to a getaway in the hot springs or these little moments with Kanuma, that seem a bit … shippy, but you're not quite sure—if anyone actually means anything by it. Natori is probably trolling (Natsume's uncharmed, exasperated reactions are always amusing, and this will be undoubtedly more so for Natori, whose acting prowess means he'll probably be more adept in discerning Natsume's fake smiles and overly polite demeanor). As for Kanuma, well Kanuma and Natsume are just really awkward, sweet people who never had friends before so -shrugs- what can you expect? But again, this open to interpretation which makes it more fun~

Please don't let it be a story where the characters get together in the end: it should be ambiguous or platonic in nature through out. Unrequited loves can be an exception. Additionally, I'll prefer if the (not quite romantic) pairings were not shounen-ai or shoujo-ai, but if the manga/anime is particularly excellent feel free to recommend.

Thanks in advance.

Hourou Musuko - the relationship between the two leads is pretty much like that...

Maybe Shutter Love and Watashi ga Itemo Inakutemo. Not sure what genres you're interested in but there are probably loads of action shounen manga that fit your description as well - Beelzebub comes to mind.

C-Blossom - Case 729
Himegimi no Tsukurikata, but it feels like it ended before something could happen

something like Satougashi no Dangan wa Uchinukenai ?

i can think of some gags that fit this description XD namely Oresama Teacher. Pulls you left and right but nothing really happens. Same with this mangaka's other work, Gekkan Shoujo Nozaki-kun (anime currently airing this season). Really, don't expect any romance even though they're tagged as romance.

Tonari no Seki-kun, another comedy. Has an anime.

Ties of Compassion for sure. Actually I have no idea why that's tagged as romance
Kuroshitsuji
Yankee-kun to Megane-chan the fact that nothing happens pissed a lot of us off XD

eeh Fairy Tail if you don't mind lots of ecchi.

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Kuragehime the anime has scenes like that at the beginning. I haven't read the manga yet to compare the two.