The price increase is not the sole basis for saying that bitcoin will become really the future of money. Though bitcoin can be used as payment online today and even in the future, it is not correct to say that bitcoin will replace fiat currency. The proper way of saying is that the future of money is digital currency. A cashless society will be born when fiat currency has finished evolving into a fiat digital currency.
You have a point here. Some people are focusing too much on the price of bitcoin and in the process still comparing it to fiat. If bitcoin is really the future of money, the value should not be based on fiat. Bitcoin is still evolving and we do not even know if bitcoin will be the end product in the future. But what we know is that, decentralized cryptocurrency is what we need. We need to get away from the control of the government regarding our finances and cryptocurrency is the answer to that.
We need a global currency before anything else
By global I mean a currency that can be used for hassle-free transacting around the world as well as without third party risks. And it just happens that decentralized currencies serve this end better than fiat currencies and their derivatives which require banks, payment processors and whatnot. With modern payment processors (i.e. exchangers like Capitalist, AdvCash, PerfectMoney, and their likes) you can transact as freely, but you are still not free from the third party risk. Essentially, you are not guaranteed that these services won't disappear tomorrow with all your money or just block your account for no reason at all (with basically the same consequences for your capital)