about algorithm

I think you mean 4, 100, and 400, not 4,100.

It's because the time that the earth takes to complete a year, i.e. to return to any given point on its orbit around the sun, is not an even multiple of the number of times it spins on its axis (a "day"). The two cycles are independent of each other.

the earth takes one year to make a complete orbit of the sun, but during that time it has spun around pretty close to 365 1/4 (three hundred sixty five and a quarter) times, i.e. it takes just about 365 1/4 days to make the orbit. We add 1 extra day each four years to compensate for that extra quarter.

But it's not exactly 1/4--it's just pretty close to that, so that extra day every four years makes the year just a smaller bit too long, so you have to skip a leap year every 100 years to get the year closer to the true value, But then you've made the year just an even smaller bit too short, so every fourth century you have to make that year a leap year again, even though it's a multiple of 100 and you would think offhand that it shouldn't be a leap year, but then you've made the year just an even smaller bit too long again, so eventually, maybe something like every two thousand year (I'm guessing on this one), you'd have to take out that leap day. Two thousand years is longer than any version of the calendar has yet lasted, so a further correction will probably have to be made sometime in the far distant future, but I'm not holding my breath waiting.

It's basically because we have to make finer and finer adjustments to a man-made creation, the calendar, which we basically think of as being a series of whole days, to make it a closer and closer approximation of a natural cycle which basically doesn't care diddly about anything humans do.

We don't determine that a year is a leap year, we arbitrarily assert that it is. Leap years don't exist independently of the human imagination.

I don't exactly agree with this. Leap years do exist to solve a real scientific problem. The earth doesn't spin an integer number of times each orbit. Any advanced civilization that keeps track of time by seasons is going to need to solve that somehow.