It's not really a race as such, at least not in this case - that's just the way the media puts things, as it makes for a good headline.

More than anything, it's wanting fall-backs and independence. Having to rely on foreign rocket builders and launch facilities is often considered a security risk, as well as risking you being put to the back of the queue if there's any delays to schedules.

Additionally a lot of countries would like to just generally build up an indigenous space industry, as it's a growing frontier for all kinds of missions (science, communications, exploration, navigation, settling, intelligence, asteroid capture, etc). It makes sense that they'd want to lay the foundations of an industry to access that area, but again it's not really a race. If you can build an industry then long-term you'll make more money on it rather than sending cash abroad, even if it takes you a while and has a bunch of failures on the way. Space is big, there's tons of room for all kinds of vehicles and organisations and missions.