Now we see the vital importance of including the word को in a sentence like this.
I think it was the Rocket Hindi course that had quite a good module on this, but it's about degrees of need - English has 'I should eat', 'I have to eat', 'I must eat', 'I need to eat', 'It's essential that I eat' etc that carry varying degrees of urgency. Hindi has the same. It's a bit arbitrary but I'd say that 'needs' (which I think would be expressed using 'zarurat' in Hindi) is a step up the urgency scale from 'has to'.
Imagine instead of "pita" it is "Barack Obama." Barack Obama is married to Michelle Obama—not Michelle Obami (even though she is female). Obama cannot change to Obami :) Likewise, we would not say "Barack Obame ko khaana hai." We would say "...Obama ko...." "Obama" will never change, despite the fact that his name ends in /a/.
Pita is like Obama :) Even though it ends in /a/, it follows the rules for words that end in a consonant.
मैं ओबामा जी से पयार करता हूँ।
Is there some reason why must isn't accepted here and in other such sentences?
See Sam362597's comment, directly above.
The word "must" in English usually carries a greater degree of urgency than is implied by the Hindi sentence. I realize that perhaps it does not sound that way in your dialect of English. But the bigger picture is that eventually in Hindi learning one will see different ways of expressing "compulsion," and it's useful to start distinguishing in how we translate.
The Hindi sentence in this example is more like a strong expectation or suggestion.
This is just a curiosity, but the distinction between "have to" and "must" is slightly more detailed than solely a question of degree. From the British Council website:
Have to shows us that the obligation comes from somebody else. It’s a law or a rule and the speaker can’t change it: Do you have to wear a uniform at your school? Must shows us that the obligation comes from the speaker. It isn’t a law or a rule: I must call my dad tonight.
Huh. I never knew that (native English speaker). So 'I have to eat' would only be correct if someone else was pressuring you to come and eat? If you're on the verge of starvation, it's 'I must eat'.
The British Council is just a language teacher of one dialect of English, not a language authority, like the Académie Française, or even a style guide. If you never knew the difference, then very likely there is no difference in your dialect of English, ad there is none in mine. Since English has no language authority, there is no source one can turn to to say the English spoken where you live is in some way sub-standard.