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Why isn't my Eevee evolving!?

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I want to evolve my Eevee in Platinum into Umbreon but he's not evolving! I walked about 9000 + 7000 + 3000 + 2000 = 21,100 steps with him! I almost never let him faint in battles and I had a soothe bell on him for a while so why isn't he evolving?

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Your math is way off, dude. 9,000+7,000+3,000+2,000=21,000.

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To evolve an Eevee into an Umbreon, you need to level it up during the night while its happiness needs to be at or above 220. While a Pokemon is holding a Soothe Bell, any increases to its happiness are raised by half of what the increase would normally be. Walking 128 steps has a 50% chance to raise the happiness of all of the Pokemon in your party by 1, or 1.5 to any Pokemon that are holding a Soothe Bell. If you took 21,100 steps while your Eevee was in your party and holding a Soothe Bell, then there were 164 total chances to raise your Eevee's happiness by 1.5. However, as there is only a 50% chance for a Pokemon's happiness to go up every 128 steps, it is unlikely that your Eevee's happiness was raised by 1.5 every single time it had the chance to. Let's say that only half of the chances to raise your Eevee's happiness were taken, so that means that your Eevee's happiness was raised 82 times. If that is the case, (Assuming that your Eevee did not have any happiness before you took the 21,100 steps.) your Eevee's happiness is 123, which is not enough happiness for it to evolve into an Umbreon. Note that 123 is most likely not your Eevee's happiness, as I had to assume that only 82 of the 164 total chances to raise its happiness were taken. Also, even if your Eevee's happiness is 220, you have to level it up during the night for it to evolve into an Umbreon.

TL;DR:
It is unlikely that taking 21,100 steps with your Eevee in your party, even if it is holding a Soothe Bell, that its happiness it high enough to allow it to evolve into an Umbreon. Also, if you know that your Eevee is happy enough to evolve, you might not have leveled up your Eevee during the night.

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Pokemon always rounds down, so a happiness gain of 1.5 will be rounded to 1. Therefore, soothe bell has no effect on taking steps. My advice is to go to the Eterna Pokemon center and talk to everyone there, and one of them will give you an app. If you open the app with Eevee in your party, tap Eevee, and hold it down, and Eevee shows two big hearts, that means the Eevee has max happiness and should evolve when leveled up.
Why isn't the 1.5 rounded to 2 is 1.5 is considered closer to 2?
I told you already. Pokemon always rounds down.