It is quite difficult to define Cantonese as a dialect as it is very distinguished from Mandarin. They are mutually unintelligible with each other. Cantonese used to say that their Language is older than PuTongHua (the official Chinese Language). There's a story about Cantonese almost become the official language of China after the XinHai Revolution in 1912 but was beaten by a small margin (Wikipedia). Whether the story is true is still arguable. Since the communist takeover in 1949, Putonghua is the common language. But since Hong Kong and Macao has not returned to China, Cantonese is the common language there.
Canton province since the Qing dynasty has been the only opening to the world, it is not surprising that many of the emigrants are Cantonese. Thus there is always an urge to define Cantonese as a language.
People in Hong Kong has always strive to distinguish themselves from Chinese. It is therefore not surprising that they actively promotes Cantonese as a Language thereby distinguishing themselves from Mandarin speaking Mainland Chinese.
There are many arguments for Cantonese as a Language.
1. Cantonese is older than Putonghua. Actually, they all developed from Middle Chinese on a different path. Putonghua is indeed developed later.
2. Tang poems are written in Cantonese. Tang poems are based on Middle Chinese. Some may have sounded more correctly in Cantonese while others simple does not sound right. Mandarin obviously does not really fit well too since Middle Chinese is used then.
3. UN has defined Cantonese as a language. UN did list Cantonese as a language together with other major spoken language of China. In the order of number of people speaking specific language in the world, Mandarin is the most (14%). Wu (Shanghainese) gets 1.2%. Yue (including Cantonese) only gets 0.89% (Wikipedia). It is undeniable that it is a language listed by UN. But saying that UN recognize it as a language (not a dialect) is a bit far fetched.
4. There are claims that UN define Cantonese as one of the six "leading language in daily use" (粵語為日常六種主要用語). It is very much doubtful this is real. Yue (including Cantonese) is 24th in the list of world's most spoken language according to Wikipedia. Wu language has even higher usage than Yue. There is no definitive link to this saying in UN.
5. Cantonese is an official language in Hong Kong, Macao. Chinese constitution 《中华人民共和国宪法》19.5 states that Putonghua is promoted as common language throughout the country. 《中华人民共和国国家通用语言文字法》section 2 states that the common language is Putonghua. Section 8 of the same article indicates each race has the freedom to develop and use their own language. Even Putonghua is only stated as national common language not "Official language". How did Cantonese being defined as "official language"? (https://www.zhihu.com/question/22600638).
It is undeniable that Cantonese is indeed a language. There is no point citing unclear or untrue facts about it as a language.