Не притворяйся, будто тебе плевать. === Don't act like you don't care.
I'm not sure how this phrase ultimately translates as "not care". I assume the omitted subject in the "будто" subordinate clause is "ты", in keeping with the preceding verb "притворяйся". So...
"ты тебе плевать"
Is this supposed to literally mean:
"you spit on yourself" === "you don't care"
I wonder, though, why "тебе" is used instead of the reflexive "себе".
“Тебе плевать.” (“You don’t care.”) follows the same pattern of impersonal sentences as “Тебе холодно/жарко” (“You’re cold/hot”). A full sentence which also sounds quite natural would be “Плевать ты хотел на это” (more or less “To spit on this is all you wanted”).
It's ruder than "Don't act as if you don't care" but less rude than "Don't act as if you don't give a sh..t". Probably similar to British 'You don't bloody care'. Literally it implies 'you spit on smth.'/ but 'on smth' is omitted. It's also possible to say that 'you spit on smb.' in other contexts (meaning 'you don't bloody care about them, what they think, do, etc.').
Relflexive "себе" is not implied here, for here the implication is that you don't care about something (you are the actor).
In the same way one can say: Не притворяйся, будто тебе это нужно. Не притворяйся, будто тебе это надо сделать, etc. (no reflexive is implied here)
If you seek rationale behind this idiom, it may be assumed that it implies a verb хочется which also requires Dative
Не притворяйся, будто тебе (хочется) плевать
The meaning of плевать as expression of disdain, denial of worthiness and indifference has been covered by other contributors.
The expression can also take the form of
плевать хотел на ... always in past tense
mostly used when speaking from the 1st person.
A synonym of плевать in this meaning is чихать or more emphatically чхать. I'll gloss over some less decent versions.
