alt Hacker NewsThe last director I had would ask "is it a day, a week, a month, or a year" he understood that's about as granular as it's possible to be.
And he really only used them in comparison to estimates for other tasks, not to set hard deadlines for anything.
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This is essentially t-shirt sizing without all the baggage that comes from time. Your boss is trying to use the relative magnitude but it's inevitable that people will (at least internally) do math like "7 day tasks is the same as one week task", or worse over-rotate on the precision you get from day/week/month, or even worse immediately map to the calendar. Suggestion: don't use time.
Knowing nothing else about him, I like him based on this alone.
I've been in planning sessions where someone would confidently declare something would take half a day, was surprised when I suggested that it would take longer then that since they were basically saying "this'll be finished mid-afternoon today"...and was still working on it like 3 weeks later.
Here's my observation: ballparking an estimate for a whole project, in my experience, tends to be more accurate than estimating each task and adding them together.
I like to think of this as 'pragmatic agile': for sure break it down into tasks in a backlog, but don't get hung up on planning it out to the Nth degree because then that becomes more waterfall and you start to lose agility.