There aren’t exactly 365 days in a (solar) year.

en.wikipedia.org/wiki/Gregorian_calendar

The Gregorian calendar is the calendar used in most parts of the world.[1][a] It went into effect in October 1582 following the papal bull Inter gravissimas issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years slightly differently to make the average calendar year 365.2425 days long rather than the Julian calendar’s 365.25 days, thus more closely approximating the 365.2422-day “tropical” or “solar” year that is determined by the Earth’s revolution around the Sun.

Because we said so… there is some science behind it, but we could have chosen different values.

I’ll just make a guess until someone more knowledgeable comes along.

To my understanding, we have the summer and winter solstices as reference points of interest. We can look at the length of shadows cast at noon to determine where you are along this cycle. When you reach the shortest length, it’s the summer solstice. When you reach the longest length, that’s the winter solstice. Count the number of days between these reference points and you have the approximate number of days in a year.

Months are arbitrary though. Someone said so, then it stuck.

A day has a fixed, non-arbitrary definition: one rotation of the planet.

A year has a fixed, non-arbitrary definition: one orbit of the planet of the sun.

365.2422 days in a year is a precise and unambiguous ratio.

A month, on the other hand, is much more ambiguous and historically influenced. Basically, the idea of a month exists around the world because we have a moon, and that moon cycles through its phases roughly about every 29.53 days. That’s the “idea” of a month. The trouble is, it isn’t really connected with either the concept of a day, nor the concept of a year… and those matter. Day and night determine when we sleep and work. A year determines the weather and when we can plant crops.

Divide 365.2422 by 29.53 and you get 12… and a bit. Pretty darn close! But annoyingly not quite exact. And that really matters for farmers especially, but also for anyone wanting to know when it’s going to snow or when the sun is going to try to kill you with heat.

Some cultures fixed this with “leap months”… varying the number of months in a year every so often in order to resync the moon and the sun. But most people these days stick with a purely solar based calendar where the months are entirely divorced from the movement of the moon. There’s still 12 months, because tradition and also because it’s a useful length of time to talk about, but the 1st of the month is not a new moon for most people.

Of course, we have leap DAYS, which are the same sort of thing. Vary the number of days in a year to resync.

But compare to midnight and noon, which are definitely based exactly on the sun. This rarely needs adjustment, and when it does, we’re talking about “leap seconds”.