Technically, it might be wrong but... a few notes: [1] It's not a sentence, just a fragment. [2] It looks OK to me - I would use it. [3] Just because it is found on an English website doesn't mean it is right - English native speakers frequently make many, many mistakes with their own writing. [4] I'm sure there are many grammatically questionable phrases in the English language, but as long as the sense is understood, they are often accepted, especially in reported speech. [5] What is the 'right' alternative you have been taught?

Shouldn't it rather be "One of the reason is (that)....."?

- One of the reasons is that ..... - This is one of the reasons why I was so late. - One of the reasons why I was late is that ... - One of the reasons for being late is ... - One of the reasons for my decision is that ...