тебе теперь всю дорогу этот грех нести. почему тебе написано в дательном падеже?

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@Datria I think what I put in my previous message is enough, but some people seem to think that it's too hard to understand. So I decided to summarize what I said and what I linked, just in case, for reference.

The subject of an infinitive sentence has to be dative. That's it, just how it works. The rest are details, if you're curious. If you have a sentence, where the verb is in infinitive form, its subject has to be in dative. If you were to rephrase the same sentence in a finite form, in some tense, then you'd put the subject in nominative, as usual.
Examples from the article:
Тебе завтра дежурить (ср. Ты завтра дежуришь);
Нам здесь не проехать (ср. Мы здесь не проедем / не сможем проехать);
Тебе бы к врачу сходить (ср. Ты бы к врачу сходил);
Не тебе жаловаться.

This kind of construction has its limits, though.
1. How it's limited in usage grammatically.
Most of the time it's used in sentences, where the infinitive is THE MAIN verb, like in your example. (решил ехать одному❌ vs. тебе одному решать👍).
But! when the infinitive is modifying a verb with a modal(ish) meaning (like want, have to, etc) it's fine. (E.g. пришлось ехать одному; хотелось сделать самому.)

2. How it's limited semantically.
Most commonly the subject would be a person/people. Sometimes it can be something else, but it's pretty uncommon and often impossible.
"Уплочено, как говорится… Ведь не гнить зерну, а? " 👍
"Температуре расти"; ?"Воде испаряться" - meh, questionable.

There are a few more examples of this construction in the article.