Why does time speed up and slow down?

There are two things called time. Clock time, where a minute is a minute, always. And felt time, which does whatever it likes - stretching in queues, vanishing in games.

There is a reason. Your brain is not a stopwatch, it is a memory machine. A stretch of time feels long when a lot of new things happened during it, and feels short when almost nothing was new. Boring waiting drags; busy fun blurs.

Here is the strange bit: this means time is not just out there in the world, it is also partly something your mind is doing. Philosophers still argue about how much of each it is.

Try it

Two-timer experiment. Set a timer for two minutes. Spend the first two minutes staring at a wall doing nothing; spend the next two doing something you love. Estimate each one before you look. Almost everyone guesses the boring one lasted longer.

What do you think?

Do you think there is a right answer to this question?

Talk about it

If nobody were bored, would time still feel slow?
Do animals feel time the way we do?
Would you rather a year that felt long or a year that was fun?

Yes, but… — the arguments people actually make

Time obviously exists. Clocks measure it.
Clocks measure a regular change, comparing one thing to another. What they measure is real; whether that is a thing called time is the question.
Ten minutes is ten minutes. Feeling differently is just a feeling.
Which do you trust when they disagree? The boring ten minutes was still, by your own memory, longer. One of the two is wrong about the same ten minutes.
If the past is gone and the future isn't here, then only now exists.
Then 'now' has to do all the work — and nothing in your body tells you when now starts and ends.

What other philosophers think

AristotleTime is the measure of change. If nothing changed anywhere, there would be nothing to measure — so time is not a container that events happen inside.
AugustineSaid that when nobody asks him what time is, he knows; the moment he tries to explain, he does not. Then he argued memory and expectation are where time lives.
J. M. E. McTaggartArgued in 1908 that time is not real at all, using only the way we talk about past, present and future.
Albert EinsteinShowed that time runs at different rates depending on how you are moving. Clock time is real, and it is stranger than it feels.

If you want to go further

Physics — AristotleBook IV. Time as the measure of change, still the position to argue against.
Confessions — AugustineBook XI, where the difficulty of saying what time is gets its best and most human treatment.
The Unreality of Time — J. M. E. McTaggart1908 paper. Overturns the obvious in ten pages.

Most of these were written for adults, which is why it is worth reading them with someone older.