I would highly suggest reading up some more on your own and reconsidering this opinion before engaging your peers @ work.
Perhaps you might want to consider backing off the Unit testing Koolaid a little and drink up a little reading on various types of testing in the software lifecycle. The whole TDD and Unit testing obsession might be well intentioned (and has potential for many benefits) but in practice is often giving new generations of developers a false sense of security.
Think of the whole application not just your little individual parts. How are you going to test your *external* dependencies? And how will your pieces of code work and interact in reality with other developers code and external services? Remember Unit tests work in *isolation* only *mocking* many interactions right? How do you intend to REALLY test those *mocked* interactions?
Hmm, this is an actual real test of your application and ideally what you WANT to do in testing: ie check whether you and your team developed a solution that actually works in real life, as opposed to mock white box testing of theory of components in isolation.
Integration testing > Unit testing
(real system components actually being tested for *real* interactions) > (mocked system components tested in isolation).
> : means it is AT LEAST as important as. Both have their place
Think of testing this way though. You want a comprehensive testing framework to ferret out as many types of bugs and issues as possible. Unit tests really only cover a small trivial subset of potential bugs. The most difficult and important bugs often come from unpredicted, unforeseen and untested interactions and effects beyond your unit level design implementation.