Of course there are some reasons not to employ Angular or someother JS framework too. Here they are in a list
Below, I'll talk about each one in more depth.
People love animations and movement and Angular allows for easy integration with CSS3 animations. Since Angular is built as a templating MVC Framework, you can animate views as they are requested by the user. By adding transitions to pages it makes the applications come alive. Things look more impressive, looking more like the web of Hollywood, than the static, drab pages of 1995. With Angular and CSS3, animate lists, divs, views - pretty much anything and bring a exciting new dimension to web sites.
One of the most appealing things about Angular is that it can allow a user to load what seems like many pages into one page. Once that initial page has been downloaded views are updated and manipulated instantaneously with Angular - there isn't any delay at all - the ap and site look snappy and responsive and generally make the end user happy with the experience. Tie in some AJAX and the site can update without having to reload any assets. Angular makes putting everything on one page a cinch. While this is a pro, it is also a con (which I'll discuss in the Con section).
People are accessing sites more and more with mobile devices - like phones and tablets. Using Angular makes your site appear more like an ap - screen to screen transitions are very app like. It also makes your site information architecture more self contained and less like website that updates from page to page. Angular adheres to a strict MVC framework that is very familiar to developers used to app development. Additionally the presentation of the site in Angular using partials and templates mean the site is automatically more modular and app like than the typical IA a website might have.
When you look at an Angular project your see folders for Models, Views and Contollers (not necessarily in that order, or named that way - but definitely grouped that way). Developers that come from a more traditional background of developing and compiling will love this type of development workflow. It is a great way to break up the website into parts that are self contained and easy to update, manage and scale. Many developers hate working on web projects because of the unruly nature of procedural, unorganized web projects. A framework automatically creates convention that is recognizable to any seasoned developer.
Using Angular could force a user into downloading unwanted information, content and code. Depending on the way a site is developed in Angular, a user is going to download content that they aren't looking for. For example a site may have many views loaded into the page, but the user is only interested in one view - that means all the additional views content was just loaded for no reason. Of course this can be avoided using Angular JS routing or with proper AJAX calls, but out of the box there is going to be some kind of waste, in the form of unused filtered results, or unused views.
If a computer is old, it may not work. Granted you might not care about a user using a Pentium 2 running Mosaic, but it is still something to consider.
This may not be the case, but depending on the usage of Angular could effect your ad revenue on a site. Typically pageviews are figured into CPC ad models. Also some ad systems will only allow so many ad instances on a page. I'm not totally sure about now, but Google Adsense used to only allowed 3 ad units per page. If that is still the case then loading all of your content into one page would really cut into potential page views. Granted this might be avoidable with use of AJAX or some other type of integration, but it is definitely something to consider if your site revenue model is based around ad views.
This shouldn't be a deal breaker, especially since MVC is such a commonly used development model, but if your dev team isn't used to developing their sites, split into templates and pieces then it could slow down your development time cycle. If you are considering Angular then I'm sure this isn't a concession.