CAPITAL LETTERS

The names of languages are always written with a capital letter.

Words that express a connection with a particular place must be capitalized when they have their literal meanings. So, for example, French must be capitalized when it means `having to do with France': 

However, it is not necessary to capitalize these words when they occur as parts of fixed phrases and don't express any direct connection with the relevant places: danish pastries, french windows, russian dressing.

When the reference is to the country, language or the people of that country, it's always capped. Always. The only time it's in question is when the nationality is being used as part of a phrase that has no direct connection to the country, and then...well, it depends. Different people and publications follow different guidelines.

Because that's what it is - a guideline. Capping the name of the country, people and language is a rule. Whether to cap the "f" in f/French dressing, d/Danish pastry, etc., is just a guideline, and when it comes to guidelines, opinions differ.