meaning - What does んだけど mean here?

「……さすがにそれはちょっと、あまりオススメできないっていうか……」

優には悪いけど、恥ずかしい……。

俺があのベッドで寝るのも恥ずかしいし、自分の部屋にあるのも恥ずかしい……。

……というか根本的な問題として置けるのか、アレは。

「なんで？　私と寝るのイヤなの？」


「いや……そういうことは全くもってない**んだけど**……」

「じゃあ問題ない、いい生活にはいい睡眠が大事」

Can anyone help me understand what it means?

In dictionaries it says that the definition for this usage of けど is 言い切りを避け、婉曲に表現する気持ちを表す but I don't understand what is being left unsaid.

Edit : Unfortunately the suggested duplicate question doesn't answer my question. The answer there literally says the same as the definition I provided. If that definition answered my question then I wouldn't have posted this question. My question is more about what is left unsaid and the function of けど in this case. Is what's left unsaid something like "けど　いやなのはそのベッドで寝ること” or is it him expressing his confusion as to why she would think that he wouldn't want to sleep together.

Answer

This sentence can translate to:

いや……そういうことは全くもってないんだけど……
No... I don't mean it, but...

Regarding the grammatical function, the けど in question is basically the same as けど described in this question: けど at the end of the sentence?

Without けど, the sentence would become 「そういうことは全くもってないよ」, which is almost equal to accepting the girl's proposal in this context (I don't know what her proposal is, but it seems to be something very embarrassing to the boy). So he hedged by adding けど. He weakened his statement by saying けど, and implied he still wanted to refuse her proposal in some way or other.

This type of けど/が/ですが/だが happens all the time in Japanese, much more frequently than in English. You don't usually have to fill "the unsaid part" because even the speaker himself is often unaware of what he wants to say after けど. It's basically just the sign of hedging. It's not always possible to fill the "unsaid part" in one way, and we can only guess from the context. That said, judging from the excerpt, my guess is that "the unsaid part" is something like 「やっぱり恥ずかしい」「それでもオススメできない」「置けるかどうかも分からない」.