Yes, you are making a mistake. Whoever told you this was correct. The only time you could say this without an article is if you were referring to 'English language' (as opposed to 'English literature') as a subject on a school curriculum or timetable - the same as 'I love geography' or 'mathematics'. It's the same with any other language: Japanese is a difficult language to learn. It's difficult to learn the Japanese language.

You can say either "I love English" or "I love the English language". You can't say "I love English language" because "language" isn't uncountable. If you said "I love an English language" or "I love English languages", it'd imply that there are many English languages. Since there's just one English language, you need to say "the English language".