Why Chinese people like to say …不了, 吃不了、去不了、买不了…

不 (bù) is used for the present and future time, as well as for habitual activities. Often the adverbs of time, including words like today, tomorrow, next week, usually, or regularly, indicate which of these is meant.

不了liǎo: can’t do something due to lack of ability.
吃不了: cannot finish the food because it’s too much
买不了：means because cannot be done。 may be that there is no money or it may be something i want to buy.
去不了：may be i have my own internal reasons

They're like fixed structures.

the phrases you mentioned are for something that cannot be done. difference like in i will not do it and cant do it

不 (bù) is used for the present and future time, as well as for habitual activities. Often the adverbs of time, including words like today, tomorrow, next week, usually, or regularly, indicate which of these is meant.

不了liǎo: can’t do something due to lack of ability.
吃不了: cannot finish the food because it’s too much

depends on how you pronounce the "了"。 do you mean "le" or "liǎo"? if it's "le", it's like a question, 吃不了(le)？do you want to eat or not? 吃不了(liǎo), I can't eat anymore. same as other phrases.