Why were some letters like Q, X, C, chosen for Pinyin which confuse non-Chinese speakers?
Pinyin, like other written systems, is an arbitrary system, and the corresponding sounds were expressly decided. It seems it was based on preexisting systems: Gwoyeu Romatzyh of 1928, Latinxua Sin Wenz of 1931, and the diacritic markings from Zhuyin (also known as Bopomofo).

But the same problem you highlight in your question happens when learning any other language. For example, I'm Italian and when learning English I had to learn that: 


"th" can have different pronunciations, that vs thick;
"ou" has several pronunciations according to the word: though, foul, through;
"c" is not just "tch" or "k" sound but also "s": center;
etc...


With Spanish, other sounds, such as "j" in joven, or with french, with "ç" in "ça va?", etc.

So why pinyin with Chinese should be different? A certain system has been decided, all that is left to do is for you to learn that system and learn to distinguish the sounds described in Pinyin from those in your language.

I think the "confusion" is for anyone that decides to learn Chinese (and therefore, Pinyin) regardless of your mother tongue (if not from asian countries): some sounds correspond to a certain language, others to another language and so on, so everyone has some advantage. The sounds that really differ are a few, and you have the same chance of finding them when learning other languages too.