The younger generations can really struggle to save money for a variety of reasons, firstly and probably most importantly is they don't earn very much to start. They will often begin in lower level retail or hospitality type jobs, because those companies want cheap workers that turnover. Secondly most people have a learning curve through life and when you're young you can be easily influenced by the media with endless marketing directed at you to buy the latest fad or even high end items. It takes a while to mature when it comes to finances. However lastly, saving a small amount is a good idea, but you should really take (reasoned) risks when you're young as you have more opportunity to make money back in future.
As a young person, it is extremely difficult to save money because, as you mentioned rightly, you are not earning much to invest or save for another day. What you earn from your labor is not commensurate with your expenditures on basic needs. So you end up earning money, but it doesn't hold much value, and it's often used to pay debts. I have been in this situation for a long time since I started managing my finances.
There are different pressing issues around me that require immediate attention, and even when I attempt to save, something important comes up that requires the money. So, it's challenging and almost impossible to save as a young person due to these reasons.