Good reasons, I must say. Although I am expecting more answers to this question, it cannot just be Egypt and Nigeria based on people's opinions.
How about South Africa? Ghana? Ivory Coast? They have a decnt football record too.
Like i already said, it is hard to pick one and it is a subjective choice. If we take a look at the countries you mentioned, they are very good footballing countries. Ghana has won the AFCON 4 times, even more times than Nigeria and they have reached the Quarter Final of the World cup, Ivory Coast has won it twice, whilst South Africa has won it once and also hosted a World Cup.
That said, if we are talking about the best African football team, based on achievements in the continent, it is definitely Egypt, there is no doubt about that. Look at what they have achieved, both in their national team and at club level, Al Ahly has won the CAF champions league a staggering 11 times, no other club even comes close.