Because the Netherlands has not adopted the EU opt-out that lets car drivers ride 125cc scooters. EU law allows member states to make a B licence valid for A1 motorcycles, but the Netherlands keeps this optional measure out of national law. So your car licence alone is not enough in the Netherlands, even if it works in Italy or Spain.
The rule comes from the Third EU Driving Licence Directive. It lets each country decide whether to extend B licences to 125cc bikes with a maximum power of 11 kW and a power-to-weight ratio of 0.1 kW/kg. Italy and Spain say yes; the Netherlands says no. This is not a mistake or an oversight. Dutch traffic policy has deliberately kept the A1 certificate separate, partly to reduce motorcycle accidents and partly because the political culture favours the existing system. That means the only legal route to a 125cc is an A1 licence.
If you have been driving a car for a while, the A1 training should not be hard. You need theory and practical exams. The practical lessons teach basic bike handling, braking, and street riding. The total cost is often in the range of 1,000 to 2,000 euros, but that depends on where you live, the school, and how quickly you learn. Ask a local driving school for a package including exams; compare two or three quotes. You can also do the training on your own scooter if you have one, as long as it is insured and roadworthy, but using a school's bike is simpler for the exam.
The alternative is to accept the 50cc limits. A 50cc moped is capped at 45 km/h, which can feel slow on faster roads. You could also look at a light electric motorcycle classified as a moped, but these still have the same speed limit. If your commute is mostly urban and under about 15 km, a 50cc may be fine. If you need to ride on 80 km/h roads, the A1 is the honest answer.
One practical middle ground: some moped models can be tuned to go faster, but that is illegal and also voids insurance. Do not do that. Another approach is to keep pushing politically. The Dutch government periodically reviews mobility rules, and other countries have changed their rules after lobbying. But do not expect a quick change.
For your specific situation, the fastest safe route is to book a few A1 lessons, even just to test whether you like it. If you already ride a 50cc, your traffic instincts will transfer. The exam is not a huge hurdle. It costs money now, but it also opens up the whole 125cc category and removes the frustration of being limited to 45 km/h.