There are the two sides of the same coin
Name of the coin is "kicking the can down the road"
Low birth rate: Capitalsim is a savage system based on dog-eats-dog. To achieve the modern levels of comfort, welfare and general wealth some western countries have (had?) and the rest aspire to, several socialist improvements from (both utopic and Marx's) communism were added to the system, such as paid holidays, limited hours timetables, sick days, unemployement benefits and pensions.
The key here is pensions. Since all of these things are paid through taxes, you can count on employed people to pay for the benefits of the unemployed, and you can count on healthy people to pay for the medical costs of the sick and injured. As long as there are more people working than unemployed or sick, the system works.
With pensions, the thing gets trickier. Unlike unemployement or illness, pension is a permanent condition - unemployement can be, but your benefits aren't, and so can be illness, but the cases are rare and the benefits small. There are two methods to paying pensions: you either save some money during your working life to spend it later (the savings method) or you pay for your elders pension when you are young and working, and you count on those who will come after you to fund yours (the redistributive method). With the first method, inflation will render all your life savings into small change unless you invest it, but there's no guarantees the investments are going to be profitable and if publicly managed is a temptation too great for politicians to milk off, and the second method is only sustainable if there are much more young people working than there are pensioners.
Most countries chose the redistribution method, but they did it at a time were people started working when they were 14yo, worked until 65yo, retired and died before hitting 70. So is they worked 50 years then benefited from pension less than 5. Nowadays these countries are finding that young people start to work (with pay and taxes) at twenty-something (in some countries, twenty-lates), retire or are retired early, before even they are 65 and then go on to live until 80 years old or more. And they need two and a half young workers to pay for every single pension. It is not sustainable anymore.
The thing is, the prospects are already dire and low birth rate make it impossible to solve. If you are 40 years old or less and live in a western country you are not going to have a pension. It's as hard as it sounds, but no politician dares to reform the pension system. Pensioners vote. Massively. And they are already way too many. The system is already broken.
Overpopulation: we are way too much people on Earth, as is evident given that all ecologic problems of the Earth are anthropogenic. There's only two solutions to this, either we reduce our numbers or we reduce our pollution footprint. The first solution can only be achieved by genocide or reducing birth rate below replacement ratio (so is, making worse the low birth rate problem we were talking about before). The second solution implies inventing not just cleaner technologies for (almost) everything we use today, but completeley biodegradable and ecologically neutral ones, which is doubtful they can even exist - the second law of thermodynamics is a hard mistress. Giving to choose, the first solution seems more acceptable, especially so if the genocide is not carried against you but by you.
We have already dodged at least one bullet - the nitrogen crisis, which was averted by Fritz Haber. It's not clear we are going to avoid the CO2 crisis (climate change) or survive the end of oil without major famines and wars.