Namibia and South Africa have a large proportion of white citizens. Of course their history is different, but both Zimbabwe and Mozambique used to have a large white population too. As far as I understand, this white population only left after the start of persecution by Mugabe in the 90's/00's and the civil war in Mozambique.
I have never heard of something like that (persecution/large civil war) in Botswana, a country that is doing better than other countries in the region, even Namibia and South Africa. Yet most white people decided to leave. Why?
Edit: alternatively, why were there never that many white peoples compared to its neighbours?
but both Zimbabwe and Mozambique used to have a large white population too.
But their white populations were never actually that much larger (percentage-wise) than that of Botswana. According to the CIA World Factbook the percentage of White people in Botswana currently lies around 3%. This may seem low, but compare this to Zimbabwe's White population, which never got much above 5% even at its peak. As for Mozambique, the proportion of White people was only around 3% at its peak as well. And that's not even accounting for the fact that Zimbabwe was the breadbasket of Africa (at least, it was until Mugabe came along...), whereas Botswana is almost entirely desert and hence not terribly suitable for settlement by European farmers.
I actually think the real question is not why Botswana has so few whites, but why Namibia, which is also predominantly desert, has so many whites.