Why is the day exactly 24 hours long?

This has got to to be the best question so far, continuing in the questions for "evolutionists" series. It disappoints me such people don't even understand the shape and structure of the very local universe.

Darwinists, if Intelligent Design isn't true, then why is a day exactly 24 hours long?

If by Darwinist you mean biologists, then you're asking the wrong group of people. Try asking some astronomers.

A (solar) day is 24 hours long because we decided to break a day up into 24 segments for the purposes of time keeping. We could have just as easily broken it into 10 hours, or 100 hours. Or even 54 hours!

Nowadays however we know that a day isn't 24 hours long. A single day can vary by around 20 seconds depending on the location of the Earth along its orbit. When closer to the Sun near perihelion solar days become longer as the Earth is moving faster in its orbit and has to rotate further to bring the Sun back to the same position on the sky and vice versa. Over the course of a year it will average out to 24 hours, although due to the Moon the Earth's rotation is decelerating.

There's also the sidereal day to take into account which is the time it takes the Earth to rotate relative to the stars. This is truest gauge of how long the Earth takes to rotate. And it is 23 hours 56 minutes and 4 seconds.

Now if the sidereal and the solar day were the same, then maybe you could invoke an intelligent designer to explain why the Earth is a relatively nice place to live, as it would look a little different to how it is now, it would have either fallen into the Sun or remain in orbit with one side boiling and the other freezing while remaining tidally locked to the Sun.

Also, the sun reaches its highest point at noon every day. Why do Darwinists claim this all happened by 'accident' and deny this evidence of intelligent Creator?

The Earth rotates and is angled away from the Sun so it has be at its highest point at some time; we decided to call this the solar noon, which when the Sun crosses the meridian (an imaginary circle crossing between the poles angled at 90° to the local horizon). If by noon you mean 12:00 then this is false. In most countries solar noon will be sometime between 11:00 and 14:00 but due to how large time zones and the fact we like taking hours off and putting them on the solar noon and 12:00 are very rarely equal unless you're stood just in the right spot.

Biologists don't claim this happened by accident. Neither do astronomers. The solar system is a product of the laws of nature. It wasn't put into place as-is by some supernatural intergalactic dictator; it developed from a cloud of hydrogen and dust over millions of years. It seems to be you like using arbitrary names or systems that we came up with to describe the universe as evidence of a designer. The only designer it is evidence for is ourselves.