First you need to remember that there are no strict rules and you can use whatever works for you. Now to clarify, there are 3 options (not 2):
ASP.NET MVC Project (your option)
ASP.NET Web Application Project (WebForms)
ASP.NET WebSite Project (WebForms as well; apparently your colleague's option)
Now, I'm greatly simplifying this, but generally both #1 and #2 share the same basic principal of being compiled/built before being deployed. This is the potential drawback that your colleague has pointed out and that's why his pick is #3. ASP.NET WebSite projects 'by design' will compile after being deployed. You can precompile them but you don't have to. Now in this context your dispute will use the same reasoning as #2 vs #3 which fortunately has been had many times:
ASP.NET Web Site or ASP.NET Web Application?
http://blogs.msdn.com/b/aspnetue/archive/2009/12/14/asp-net-web-application-projects-vs-web-site-projects-in-visual-studio.aspx
On a side note I dare to guess that your colleague is a certified MS tech guy as this kind of question appears frequently on MS ASP.NET exams. From my experience I can only tell that these guidelines Microsoft has set for choosing web projects never actually got me convinced. They say it depends on project and team style, however in my professional experience I never had the chance to see the ASP.NET WebSite projects's 'advantages' paying off in practice.
Keep in mind we're only speaking about precompiled vs non-precompiled (your colleague's argument) and there is much more than this between ASP.NET MVC and WebForms.