The problem statement
Congratulations, you've built an amazing web application!
But people hate it because you keep shipping bugs.
You have only so much time to dedicate to your project. Even if you're spending 100% of your waking moments working on your product, you'll always have this limiting factor: time. You need to focus on activities that will give you the biggest return on your investment of time.
If you skip on testing, you'll inevitably spend more time fixing bugs. The bugs shipped will also result in customer churn, so you'll spend more time looking for customers you won't be able to retain. Writing automated tests is just as important as writing the code that makes your app work. It operates under the same currency (your time), and pays for itself in time saved. That is... if you do it right.