qnmaster
That's their PR message, not their goal. They were pretty clearly social attacks trying to coopt the name.
That's what it solves. It removes the need for trust and dependence in a central authority. There's no central actor to hack, or that can abuse the system, or be compelled to censor.
Consider Paypal. They're obligated to follow the regulations of every single government whose citizens they serve. Paypal themselves can also make value judgements. That severely limits who can use the system, for what purposes, in what quantities, and how frequently.
That's called a Sybil attack, and yes that's one of the reasons.
Mining also makes creating blocks have a real world energy cost. So rewriting history quickly becomes almost impossible as blocks are added. An attacker would have to have more than 50% of all mining power for a sustained period of time.
I suggest reading the Bitcoin whitepaper, it's short and sweet.