This goes back to two related but very different meanings of the verb confuse
One meaning of confuse takes two objects, call them A and B. To confuse A and B means to “mix them up”, to mistake A for B and B for A.
I always confuse Amy and her sister Barbara. Which is the one with green eyes?
In this sense we also say confuse A with B.
I think you are confusing Argentina with Brazil. They speak Spanish in Argentina, but Portuguese in Brazil.
When you turn confuse into the noun confusion, you should use of to designate its two objects.
My confusion of Amy and Barbara got me in big trouble when I brought Amy a present on Barbara’s birthday.
The other meaning of confuse is to “bewilder” or “puzzle” someone—usually a person, but an animal can be confused as well.
Carol confuses me. I can never tell whether she she’s really angry or just joking.
His sudden shout confused the bear, which turned to see where the sound came from.
When you say “I am confused”, you are using this sense in the passive voice: something confuses you. We have two ways of designating that ‘something’: either with by or with about.
- Use by when you are talking about something which you feel is in some way responsible for your confusion, something which ‘actively’ confuses you: a person for instance, or a text.
I am confused by this passage in Macbeth. I can’t make out what he is saying.
- Use about when you feel that it is you or your misunderstanding which is responsible for the confusion.
I am confused about when to use to doing.
But we never use of with confuse or confusion in this sense:
∗ I am confused of when to use to doing.
When you use the noun confusion on ELL, chances are that you are confused about something. Occasionally you will be asking how to avoid confusion of one thing with another. And every once in a while an Answerer will point out that confusion is created by a speaker or writer or teacher:
I cannot blame you for being confused by this definition of the past perfect. It is entirely wrong. Throw that book away. Read what FumbleFingers says instead.
The question you have added addresses a different verb, which uses prepositions quite differently. (This is usually the case; you can almost never generalize from the use of a preposition in one context to its use in other contexts.)
Think, again, has two different meanings. One is to “examine a matter mentally”; in this sense, the matter you are examining may be expressed with either of or about.
I’m thinking of you all the time.
I’m thinking about you all the time. ... these two mean the same thing.
The other meaning of think is to “hold an opinion concerning something”. In a question, we use either about or of to designate the something:
What do you think of The Fountainhead?
What do you think about The Fountainhead?
But in statements we use of, complemented by an as phrase; or no preposition complemented by a nominal or adjective phrase; or a full clause, finite or non-finite. We never use about.
okI think of it as one of the seminal works of modern philosophy. (a very rare use)
okI think it pretentious and jejune. (an occasional use)
okI think it is preposterous rubbish. (the most common use)
okI think it to be repulsive and unreadable. (a rare use)
∗ I think about it a vile threat to our democratic institutions. (an unacceptable use)
∗ marks a usage as unacceptable