There are all sorts of pros and cons on both sides of the argument. There is no smoking gun argument, or else the competition wouldn't exist.
I get annoying Apple haters every so often... and I just tell them "I like my phone. It is a good phone. Do you like your phone? I'm sure it is a nice phone. Why do you care what I buy?" That usually ends those annoying conversations.
If you're interested having an actual conversation with your coworkers though, here are a couple of my "go to" responses:
1) Having one company that designs both the hardware and the software to work seamlessly together creates a smoother overall experience. There is all sorts of data out there that shows how iPhones, despite their "lower specs" are faster and more efficient than the competition.
2) iOS is far safer than Andriod when it comes to malware and the like.
3) Apple doesn't sell my information. Why is Apple considered "evil", compared to Google?
4) I like Apple's integration through my other Apple products (OSX, AppleTV, AppleWatch), that an Android phone doesn't offer me.
5) I don't need a fully customized operating system. I need something that works reliably. iOS offers that. I'm very familiar with it, and I don't see many incredibly useful advantages to switching at this point.
At the end of the day, there are nice products out there that don't have an Apple logo on them. If some of the features in those other products make someone want a non-Apple product, good for them. But I've never understood the need to argue, or to convince other people that they've chosen the "wrong" phone... so that's why I usually stick with the initial response.