An NPN transistor can be "viewed" as two junction diodes connected together but the p region is much thinner than the two N regions. When the transistor is under bias or in active region the BE junction is forward biased, allowing the majority charge carriers in the emitter (n) to inject into the base. When the transistor is under bias or in active region the BC junction is reverse biased, preventing the majority charge carriers in the collector (n) from injecting into the base. So, all charge carriers come from the emitter (thus the name emitter). Why do they make through a reverse biased BC junction? Well, over 90% of the charges make through, not because they are up against any obstacles, because they are not. The electric field in the reverse biased BC junction helps the electrons move towards the collector, not prevent them.
The reason a semiconductor diode only conducts one way is because its charge carriers (majority) only move one way when forward biased, eg. holes go from anode to cathode, or electrons from cathode to anode, much like the vacuum tube diode. If you reverse bias, majority charge carriers are pushed the wrong way by the reverse bias while the minority charge carriers are pushed the current way to conduct. But there are not enough minority charge carriers so conduction is next to nothing. If you hypothetically inject a bunch of say electrons in the p region of a reverse biased p-n diode, with a syringe, you will see significant conduction until the electrons are used up or recombined with holes.
The reason a transistor conducts even when the CB junction is reverse biased is because of the injected charge carriers from the emitter do the conduction, through the reverse biased junction. If left alone without emitter to inject charges, the reverse biased CB junction will simply not conduct. That is why the base is made much less doped and much thinner than the emitter so that the injected charges make to the CB junction without much loss and do the conduction.
It’s like the USA is in such urgent need for STEM people but they themselves are so reverse biased from doing STEM, they have to inject STEM people from other countries to keep their high-tech industry flowing. If foreign talents stop coming to the USA, their high-tech industry will likely suffer, under the current negligence of STEM education of the public.