I get into this argument with my coworkers from time to time, and I have to say I disagree a million percent. Tests are the only way you can see if the software is going to work.
After you make a change, how do you make sure the software works? By trying it out? Congratulations! That's testing! Now you just need to invest some mental effort in teaching the computer how to do that test for you, and now you can automatically achieve the same level of safety that you had before.
I'm all for code reviews too, but code reviews do not scale the way that tests do.