With installing Google Play Store you also install some Google services (for automatic updates, location services, etc.). Some might be afraid to do that for privacy reasons.

If you only want some specific app from the Play Store it's easier to get the .apk only from such a service. However, you won't get any update notification this way.

By the way, for open source Android software, F-Droid is a great alternative. The installation process is not as invasive as the Google Play Store, you only need a single .apk from their website.