There are three good reasons for this:

1. The harder work an uphill hiker has to do
2. The smaller field of vision of an uphill hiker
3. They are in that "hiking rhythm" zone which shouldn't be interrupted

This paragraph contains everything you need to know:

And most important and most ignored, everything else being equal, give the right of way to the hiker going uphill!

Why the latter? Think about how most people hike - usually focused downward, a few feet ahead on the trail, watching their footing to try to avoid a face plant. If you're headed downhill, you'll generally see some distance ahead of you on the trail at the same time as you're looking down to where you will set your feet the next step or two. You'll see any hiker coming up hill well in advance of meeting. On the other hand, if you're hiking uphill, and looking down at the trail, your range of vision is really just a few feet in front of you. Clearly the hiker going downhill has the visual advantage, and time, to adjust his position so the uphill hiker can pass. And, it's a lot easier for the downhill hiker to stop and resume than it is for the uphill hiker. Think about the interstate trucker or you on a bike - it takes more energy and time to restore speed if starting from a dead stop. So it is with the uphill hiker, especially if carrying a backpack - let her come on through so she can benefit from the "body in motion" principle in physics. This applies to hikers running downhill too. And just because you're running downhill (nobody is impressed anyway, and secretly hoping you face plant) that doesn't give you the right of way.

From Lowergear - Who has the "Right-of-Way"?

Further citation:

On a narrow pass, hikers going uphill have the right of way. Simply put, hikers moving uphill are generally working harder than those on the downhill slope. It is courteous to move to the side and let the uphill trekkers pass through.

From Phoenix New Times - Hiking Etiquette

It seems that many hikers—even experienced ones—may not know or always remember this, but hikers going uphill have the right of way. This is because in general hikers heading up an incline have a smaller field of vision and may also be in that “hiking rhythm” zone and not in the mood to break their pace. Often an uphill hiker may let others come downhill while they take a breather, but remember that’s the uphill hiker’s call.

Form Co-Op Journal - Trail Etiquette

There are three good reasons for this:

1. The harder work an uphill hiker has to do
2. The smaller field of vision of an uphill hiker
3. They are in that "hiking rhythm" zone which shouldn't be interrupted (Inertia)

This paragraph contains everything you need to know:

And most important and most ignored, everything else being equal, give the right of way to the hiker going uphill!

Why the latter? Think about how most people hike - usually focused downward, a few feet ahead on the trail, watching their footing to try to avoid a face plant. If you're headed downhill, you'll generally see some distance ahead of you on the trail at the same time as you're looking down to where you will set your feet the next step or two. You'll see any hiker coming up hill well in advance of meeting. On the other hand, if you're hiking uphill, and looking down at the trail, your range of vision is really just a few feet in front of you. Clearly the hiker going downhill has the visual advantage, and time, to adjust his position so the uphill hiker can pass. And, it's a lot easier for the downhill hiker to stop and resume than it is for the uphill hiker. Think about the interstate trucker or you on a bike - it takes more energy and time to restore speed if starting from a dead stop. So it is with the uphill hiker, especially if carrying a backpack - let her come on through so she can benefit from the "body in motion" principle in physics. This applies to hikers running downhill too. And just because you're running downhill (nobody is impressed anyway, and secretly hoping you face plant) that doesn't give you the right of way.

From Lowergear - Who has the "Right-of-Way"?

Further citation:

On a narrow pass, hikers going uphill have the right of way. Simply put, hikers moving uphill are generally working harder than those on the downhill slope. It is courteous to move to the side and let the uphill trekkers pass through.

From Phoenix New Times - Hiking Etiquette

It seems that many hikers—even experienced ones—may not know or always remember this, but hikers going uphill have the right of way. This is because in general hikers heading up an incline have a smaller field of vision and may also be in that “hiking rhythm” zone and not in the mood to break their pace. Often an uphill hiker may let others come downhill while they take a breather, but remember that’s the uphill hiker’s call.

Form Co-Op Journal - Trail Etiquette