You are absolutely correct, stable source of income is not a criteria someone ought to meet before they can invest in Bitcoin but it is good to have a stable source of income because if you are focused and determined to hold for long time, stable source of income will help you get there ( desire target) without much pressure because you will be able to allocate funds to different needs and wants and at same time grow your discretionary and emergency funds because these two are the ultimate for a healthy and smooth investment but regardless someone without this stable source of income can still do all these if they are very conscious about their investment and how to use their funds.
Well the both of you are misunderstanding what having a stable income can do for you when your investing. And you're also neglecting the fact that you cant keep up with your investment for a long term when you dont have a stable source of income. The reason why a stable source of income is important is not because of the investment alone, its because of the necessary things you must do before thinking about investment. I believe you know them. Without a stable source of income, you can't have an emergency fund, savings, and funds to care for your basic needs, talk more of to have discretionary income. It might make you want to tamper your investment.
as far as am concern what you need to is a source of income and not a steady source of income to start investing in bitcoin, remember you are to invest only your leftover money (discretionary income) so if you can be able to map out your discretionary income from your source of income then you can get started with bitcoin, start accumulating bitcoin until you reach your accumulating target and then hold it for long term 4 to 10 years or longer. Steady source of income is not not needed to get started with bitcoin, just have a source of income and then map out your discretionary income to invest in bitcoin and also to build up your emergency fund and backup fund for smooth running of your bitcoin investment for the long term.