For starters, the recorder is a great instrument that is played by everyone from the absolute beginner up to conservatory-trained professionals. There are some differences in how it is used in European compared to American culture--for starters, almost all professional-level players hail from outside of the US, whereas in the United States it is seen primarily as a pedagogical tool.
The reasons for this, then, are many:
- Recorders are cheap
- They are not easily breakable
- They are light and don't require a specialized embouchure, making them usable as a starter instrument for other wind instruments
- They come in a few different sizes, so ensemble/choir music can be played without teaching new instruments.
- Tons of pedagogical materials exist for recorder as a result of the above reasons1
Besides the physical considerations, I wouldn't necessarily say the recorder is easier to play than other wind instruments; as with many "easy" instruments, they are only easy to play badly.
To further explain the third point, we need to consider the typical ages where different instruments are introduced into the music curriculum (there are always variations; I will reference what is typically practiced in much of the US). The reasoning behind this progression actually has to do with the muscle coordination development of young students:
- Prior to 3rd grade, students will mostly be playing Orff instruments, which are percussion instruments that don't require fine muscle control in order to play.
- By 3rd grade, most students have developed fine motor control to the point where the recorder is a viable option, so it is typically introduced into general music curricula at this time.
- Band programs start either in 4th or 5th grade. These instruments are necessarily more difficult to play than the recorder, as they are larger and heavier, and require specialized embouchures.
So to recap, the recorder is used to teach instrumental note reading to all general music students, and also as an introductory instrument in the year or two before the band instruments become physically viable for students.
So, I don't know why "parents" like the recorder, as in my experience American parents don't have much of an opinion, and it really isn't a matter of choosing between the recorder and a different instrument; rather, the recorder is being used in general music classrooms with all students to teach relevant skills at that time. I imagine in Europe the reason for the different perspective is the greater prevalence of classical recorder players, and a different curricular use of recorder as an introduction to other wind instruments.
1 see also: "Recorder Karate"