How to ask your boss for time off
Ask about the impact, not about permission.
The situation
You have dates in mind and you are drafting something apologetic. The apologetic version invites scrutiny, because it implies you are unsure whether you should be asking.
The version that works states the dates, shows you have thought about coverage, and asks about the impact rather than for approval.
Why it is hard
Requests phrased tentatively invite the reader to supply the missing confidence — usually by asking questions you did not want. In politeness terms an over-hedged request signals that you consider the imposition large, which primes your manager to treat it that way. Stating dates plainly while showing coverage frames it as a planning conversation rather than a favour.
What to actually write
Two versions of the same message. Same facts, different posture — which one is right depends on the relationship, not on which is “better”.
Common questions
Do I have to give a reason?
Usually not, and offering one invites it to be weighed. "A family commitment" is sufficient where any reason is expected at all.
What if it is short notice?
Acknowledge it in one clause and lead with coverage. Short notice is forgiven when the gap is already filled.