Pursuing both together is wrong because you must do it well whatever you do. If you do not choose a school, you must study well. For this, it is very wrong to focus on something else. On the other hand, when it comes to acquiring skills, it is seen that you cannot devote time to studying well. It is challenging to pursue both together, but even in this, many people who can work very hard do so. However, it would be best to choose one of them carefully. First, you should focus on educational qualifications and move towards acquiring skills. I think it is foolish to acquire skills without considering educational qualifications.
It is not foolish to acquire skills without proper education, but it's better if you can have both. Many people don't get to complete their degrees or have a proper academic qualification, but they tend to become skilful in something as time goes by. We often see people trying to have skills other than what their major has actually been, and it's because our interests may shift over time, maybe because of the scope we see in other industries, or maybe because we were forced to choose a major that we never liked in the first place.
In today's world, having an academic degree is not as important as it is to have proper skills to succeed. I know we shouldn't always look up to these things, but many very successful and wealthy people in the world never completed their college; Mark Zuckerberg is one name among them.
So, it's all about learning things that can make you reach a higher place in life, and that can be achieved even without a degree if you are ambitious and hard working.