Firstly, make sure that you have a reliable network connection while downloading WhatsApp from Play Store or App Store. There are times when users are not able to install WhatsApp on their system due to lack of storage.
Go to your phone’s Settings > About Phone and check whether it is running on a version of the OS that is compatible with WhatsApp or not. For instance, it no longer supports devices running on Android 2.2 and older versions. If your phone is running on an older version of iOS or Android, then chances are that WhatsApp won’t support your device. There could be plenty of reasons for not being able to install WhatsApp on your phone.