"More roads encourage more drivers"
Roads allow more people to do what they want to do. If we can eliminate the bad things about individually controlled transport (road noise, inefficient petroleum based power, huge parking lots, etc) why should we not let people have this great thing they desire. Are you anti-democratic?
Driving is not free. It takes time and money for gas and wears out your vehicle. People don't (generally) just drive around for the hell of it, especially at commute times when the roads a most full.
"the people on public transport are not 'random strangers', they are members of your community"
This I think is the main reason some people want public transportation to be mandatory. Somehow being forced to be with other people (who are all on their phones, desperately pretending no one else exists) is a good thing? Standing up for 40 minutes packed, hot, and smelly. Occasionally aggressive beggars; homeless people who stink up the entire train car sleeping; mentally ill people yelling at the ether, etc. Not all the time but at least once a month if you are a commuter. I guess it is a cool experience to have to see how the other half live, but a some point many people don't desire such things.
"backpack"
For the human race to continue, each couple must have greater than 2 children. Try taking 3 children under the age of ten by your self, walking to a bus stop, getting on the bus, getting on BART, walking to the doctors appointment, and then back again. Basically impossible.