Two things.
First, you're responding to a factual argument with an argument about my attitude. It is not "my attitude" that people "shouldn't" be entitled to test applications. It is a fact that they are not allowed to do that. Unauthorized access to computer systems, which has a broad but actually very straightforward definition, is unlawful. If you cause damages when you do it, you're liable for civil damages. If you attempt in any way to profit from having done it, you're liable for a felony charge.
Second, arguing about this stuff by analogy is perilous. You can see that here, because it's immediately obvious that observing your child's caretaker eating lunch is not comparable to breaking into a web application to steal a database over the span of several days. To attempt to equalize the analogy, imagine that instead of simply observing your child's caretaker, you instead break into that caretaker's residence or place of work. You've now committed a felony.
I am for many obvious reasons pro- security testing, and I'm happy to speak glowingly of the companies that have set up policies to make it safer for researchers to test their sites. In advice I've provided on HN and to startups, I've consistently told companies to create pages to thank security researchers.
Having said all that: if you don't have permission to test someone's web app, don't do it. The law very reasonably says that if a company doesn't want to submit itself to unauthorized intrusive testing by strangers, it is entitled to treat its applications, its servers, and the data it holds as private property. Not every case in which a stranger pokes for flaws in someone's app will be open- and- shut, and that's for the best too. But the rule of thumb is very simple: leave other people's apps alone.