Also please note most millionaires in the world are self made, with over 80%. Of the other 20% most made it to millionaire status before receiving an inheritance. Also note the people you most worry about, the ones who get money young, usually plow through it and leave nothing for their children.
Unless someone was born into poverty and fought their way out, I don't count them as self made. No doubt these people exist, but it would never be 80%.
There's also a stronger social safety net in many countries that are poorer than the US, where you certainly don't have to worry about not getting to college (if you have good enough grades) due to family income.
Binary categories such as "self-made" vs "not-self made" fit poorly in the real world and suffer due to each individual having a different threshold of self-madeness. For some people it means not having directly inherited a lump sum, for others it means having made every single cent without outside help.
But the key thing is if he'd failed, he had a cushion to fall back on. Had Microsoft gone the same way as many other computer companies, he could be confident he wouldn't end up on the streets.
You cannot just state one thing from the side of later comer, and later switch to the side of early comer. That way you are saying 2 things...
The first was recognizing that that inheritance mostly came from the labors of someone and they have a right to do with their money as they see fit. The second is acknowledging that the person who didn't work for their wealth usually squanders it so don't waste time being jealous of them.
So focus on being the person who creates wealth for themselves and try to educate your children so they will have good money habits later on in life and will squander less of what you leave them.
I'd be more sympathetic to inheritance if the primary source of taxation was wealth.