Expound and simplify the "semantic progression" behind "must"?
I don't understand the "semantic progression" that I emboldened. The steps in the "semantic progression" feel farfetched and unconnected to me. Can someone please fill in, and elaborate, the steps? I try to explain my bafflement.
1→2. If you've measured out time for doing something, then you definitely have time to do something. Correct?
2→3. Just because you have time to do something, doesn't mean you are able to do something. Theoretically wealthy retirees have time to learn Algebraic Geometry, but perhaps they're innumerate, senile, and incapable of learning the math.
3→4. Just because you're able to do something, doesn't mean you're allowed to do something. Most physicians know how to assist patients with euthanasia, but medically assisted suicide is illegal in many countries.
4→5. Just because you're allowed to do something, doesn't mean you HAVE to do it! Every adult is allowed to reproduce 20 kids, but you don't HAVE to!
English has three words must. By far the commonest is of course the verb, ‘have to’ [OE], which originated in Old English as the past tense of the now obsolete mūt ‘may, must’. It has relatives in German muss and Dutch moet, but its ultimate origins are not known for certain (there may be some distant link with Germanic ‘measure’-words, such as English mete, suggesting a semantic progression from [1.] an original ‘time measured out for doing something’, through [2.] ‘have time to do something’, [3.] ‘be able to do something’, and [4.] ‘be allowed to do something’ to [5.] ‘have to do something’).
Must ‘unfermented grape juice for making into wine’ [OE] comes from Latin mustum ‘new wine’, a noun use of the adjective mustus ‘new’. Mustard is a derivative. And the esoteric must ‘sexual frenzy in elephants, camels, etc’  comes via Urdu from Persian mast ‘drunk’.
Word Origins (2005 2e) by John Ayto. p 343 Left column.