Parents just want to protect you from making irrational decisions. Making irrational decisions is habit forming so they are trying to get you into a good habit. By making you justify to them why you need something, it will form a habit that you will continue throughout your life, but you won't be answering to your parents, you'll be answering to yourself and taking responsibility for you and your family. You'll look back on this someday and say "damn, I sure am thankful that my parents taught me to think about my purchases thouroughly".
Also, since you are young, this may not be easy to comprehend, but we should not be in business to buy equipment. We are in business to make money. For example I could use a new walk behind cause mine is starting to require occassional tinkering, but it still works and cuts well. I could get a new one and improve my productivity slightly, but that would cut directly into my "take home" money. The longer I can productivly use this mower the better return on investment in the mower.
Someday, If you are successful, you will be able to make a very good living and support a family with what you are making. Just remember that you should be putting some money aside for yourself and some for the business, not just working your balls off for new equipment. It sounds like you are well on your way to a very successful business.