When a non Muslim learns that Muslims are required to pray at particular times of the day, his reply was you should be able to decide for yourself when to pray. For example, Perhaps you are busy today or tired so you pray less and pray more on other days. Basically you choose how many times to pray per day and when. Why is this not a good idea from an Islamic perspective?
The daily prayer times are "prescribed" in Islam, i.e., Muslims believe that they are required by Allah to perform their prayers at certain times. The Qur'an doesn't directly tell us to pray at precisely these times, but the requirements have been passed down from Muhammad or deduced from Islamic literature by scholars (see e.g. Islam Q&A).
There's some flexibility:
- usually there's a window of an hour to a few hours (it varies with the location of the sun, however),
- it's permissible for a traveller to pray fewer prayers (Qur'an 4:101),
- women with menses do not pray (see Islam Q&A),
- praying on a flight is more relaxed (see Islam Q&A),
- sometimes Muslims "merge" prayers (performing the same prayers, but in three batches rather than five), which is common when someone has a commitment, and (from my experience) is normal in Shia Islam (see Al-Islam).
So Muslims have some ability to choose for themselves when to pray. Nevertheless, it's generally best to pray (punctually) just after the appointed time. Also, if you're really in a hurry, it's possible to pray quickly. When you're prepared in advance and know what to do, it doesn't take all that long.