One of the most prevalent arguments against the Hayate x Nagi ship is that Hayate has never shown any "romantic attraction" towards Nagi.
Unlike almost every other girl in his harem, Hayate has never seen Nagi as someone that, to put it crudely, he might want to have sex with.
Now you might think that this is a pretty crazy argument, but I can assure you that there are people out there who have explicitly mentioned this as one of the most compelling reasons why Hayate should not have ended up with Nagi. Because Hayate has not shown any sexual attraction towards Nagi (read as "romantic love"), it is therefore very "forced" that he should suddenly fall in love with her at the end of the series.
Apparently, wanting to have sex with someone is the only way one can truly fall in love with someone in a romantic sense. Well, it is true that sexual attraction has some degree of importance -- but I don't believe we should close our doors to the idea that someone can fall in love in a romantic sense with another person and without ever getting sexual about it. While I am not an asexual individual, I think we're placing a bit too much importance on sex in a fictional story in a manga that makes no pretense about being realistic. Yes, Hayate no Gotoku has some relatable characters with some degree of realism, but to claim that their relationships are realistic rather than idealized would be pretty bold indeed.
It would seem that you're conflating love and lust quite a bit if you think this way.
Personally, I have no qualms about admitting that I am in love with Nagi and yes, that includes being sexually attracted to her -- but that is not what initially made me like her. Consider this saying:
"You fall in love with the little things about
someone, like the sound of their laughter
and the way their smile forms."
So yes, it's the little things that really made me fall for her. Those little personality quirks she has, the way she talks in a high and mighty manner, her cute little ways, that domineering attitude, her sincerity and kindness, and yes, even the way she smiles.
Now, look back on the manga and take a good look at Hayate's eyes whenever he's looking at Nagi's smile or remembering something about Nagi. His eyes look almost the same every time -- and it is exactly the way he was looking at her back in the penultimate chapter of the manga as well.
Suffice it to say, if Hata says he meant for Hayate to fall in love with Nagi eventually, then perhaps he really did leave those little clues behind in the manga for us observant readers to find.
Of course, if you're not that observant, then you need the crutch of explicit, direct storytelling and lines like "At that moment, Hayate Ayasaki had fallen in love with Nagi" or something to that effect, right?
Well, not that it matters. We Nagi shippers were never looking for that type of narrative in the first place. There was always something special about the bond between Hayate and Nagi since day one and it's really gratifying to know that it was indeed love all along.