In my country, I learned to-infinitive has three kinds. I am not sure these terminology, so I will introduce usage of .
One is usage of noun. For example, it is difficult for you to solve.
Another is usage of adjective. For example, I have to quit smoking to make me sick.
The other is usage of adverb. This type has a lot of usage like common adverb. However, I will say only one example, which is about "(in order) to". For example, In order to get good grade, studying hard is necessary.
When I was in Boston, my English teacher graduated from Harvard taught me that "STARTING WITH TO-INFINITIVE IS WRONG, SO PEOPLE WRITES IN ORDER TO, RATHER just TO." My teacher said like this. (Not exactly same.)
However, I see many sentences in papers with starting with TO. Surely, teacher said there are a few exception like "to be honest", and "to begin with,". And she added speaking to "However, people use "Speaking frankly" rather than "to speak frankly" in the head of sentence.
What is true? Do I have to reject to use "to-infinitive" in starting part of sentence?