For me, it is simply because I would like to take control of my limited time on earth.
Finally, I believe everyone is already investing. Everyday we are making decisions on how to use our limited time and money resources. Hence we might as well learn to optimize this decision-making process to achieve the maximum value.
Interesting question. Firstly, I guess it depends on how we define “invest” here. If we are strictly talking about financial market, then I can think of a couple of reasons why one should not invest. Otherwise, I strongly believe everyone should always invest including oneself.
Why you should not invest in financial market
You still have debts that have likely higher interests than the returns possible from investing.
You have opportunities from other type of markets (e.g. business opportunities) beyond financial market which have better expected returns.
You do not have spare monetary resources after deducting basic needs. This is more debatable because definition of needs can be fuzzy and personal. (e.g. While housing is a basic needs, what is the minimum size one needs?) This is when I believe one should invest in oneself (e.g. education) to significantly increase their income.