It's actually supposed to be type of fan. On the Wikipedia page where Japanese War Fans it says:
In addition the symbol of the Uchiha Clan is a fan which is a reference to uchiwa (団扇, paper fan) which is another way of pronouncing the clan's name.
Source: Japanese war fan - In popular culture (2nd Paragraph)
Looking at the Wikipedia page for the Uchiwa (and even googling it) we can see that the Uchiha Clan Symbol is shaped like that of a Uchiwa.
This is also backed up on the Naruto Wikia also giving a logical reason why it's also a fan.
"Uchiha" is another way of pronouncing "uchiwa" (団扇, paper fan), which is the clan's symbol. Uchiwa can be used to fan flames, making the flame hotter — referring to the fact that the Uchiha is a clan of Fire Release users.
Source: Uchiha Clan - Trivia (first point)
This also allows us to infer as to why the colour scheme is by chance like a Pokeball. A Flame is generally seen as red however the hotter a flame gets the closer it'll get to being white.
The colder part of a diffusion (incomplete combustion) flame will be red, transitioning to orange, yellow, and white as the temperature increases as evidenced by changes in the black-body radiation spectrum. For a given flame's region, the closer to white on this scale, the hotter that section of the flame is.
Source: Wikipedia - Flame - Flame Colour (3rd Paragraph)
Now given that a flame is generally hotter at the source one interpretation could be that because the bottom part is supposed to be a Uchiwa handle this would be the hottest part (being in your hand all the time).
Another interpretation could be that while also being an Uchiwa the symbol also looks like how some Flame Release Jutsu's get "spat out".
So the "handle" is the jet of fire coming from the mouth, since fire is normally hotter at the source this part would be white while further away it would be red.