1. It's dangerous.
Wander around the wrong parts of Johannesburg or Nairobi and you could get into trouble, but the same can be said of almost every city on the planet. Most of your African Safari will be spent in the bush. You are safer there than in your own home, unless you try to hug a hyena or something.
2. I'm likely to be robbed.
Nope. You are more likely to be robbed on a Caribbean holiday, or on a trip to Florence, Rome, Prague, Budapest, Mexico or Thailand.
3. The food will be terrible.