Aeroplane and airplane

Solution 1:

Wikipedia defines the reason:

Aeroplane, originally a French loanword with a different meaning, is the [older spelling.][4] The oldest recorded uses of the spelling airplane are British.[4] According to the [OED,][5] "[a]irplane became the standard American term (replacing aeroplane) after this was adopted by the National Advisory Committee for Aeronautics in 1916. Although A. Lloyd James recommended its adoption by the BBC in 1928, it has until recently been no more than an occasional form in British English." In the [British National Corpus,][6] aeroplane outnumbers airplane by more than 7:1 in the UK. The case is similar for the British [aerodrome][7] and American [airdrome,][8] although both of these terms are now obsolete. Aerodrome is used merely as a technical term in all of Canada, Australia, and New Zealand. The prefixes aero- and air- both mean air, with the first coming from the Ancient Greek word ἀήρ (āēr). Thus, the prefix appears in aeronautics, aerostatics, aerodynamics, aeronautical engineering, and so on, while the second occurs (invariably) in aircraft, airport, airliner, airmail etc. In Canada, airplane is more common than aeroplane, although aeroplane is not unknown, especially in parts of French Canada (where it is however used only in English – the French term is avion, and the French word aéroplane designates 19th-century flying machines)

[4][http://www.etymonline.com/index.php?search=aeroplane&searchmode=none]
[5][Oxford English Dictionary, airplane, draft revision March 2008; airplane is labeled "chiefly North American"]
[6][ British National Corpus. Retrieved 1 April 2008]
[7][Merriam-Webster online, aerodrome. Retrieved 1 April 2008.]
[8][Oxford English Dictionary, airdrome.]
[9][http://www.merriam-webster.com/dictionary/aeroplane]

Solution 2:

Etymology online says

1907, from air (1) + plane; though the original references are British, the word caught on in Amer.Eng., where it largely superseded earlier aeroplane (1873, and still common in British Eng.; q.v.).

so I guess your real question is why "airplane" caught on better. It could be the a more common spelling, a simpler connection with "air", which is an English word as opposed to more complex connection to foreign "aero".

However, this is such a nice question to show some ngrams.
British English corpus: American English corpus:

There you can see that even in American English it started as a more common word, until replaced in 1920s when airplane overtook.

Solution 3:

Airplane is a US simplification of aeroplane, aeroplane having come from the French word aéroplane. The simplification came about because of a combination of people not wanting to bother with the 'o' sound at the end of 'aero', and perhaps a genuine misunderstanding that the aero- prefix is intended. People have have suspected that, as the thing travels through the air, the prefix ought to be air- for airplane.

As to your aside; yes, I suspect you do prefer that pronunciation because it's the British one. :-)