Teachers have a limited range of activities in a one to one classroom. Most activities require the interactions of multiple students. Without group work of any kind, teachers must continually think of activities he can do alone with the student. Furthermore, there is likely a shortage of materials in a one to one setting if student and teacher do not meet in an actual classroom, where there are plenty of materials available.
There are not many situations in life where you spend an hour or two alone with just one other person. This can become boring for both the teacher and students if the teacher does not constantly initiate new activities and drive the teaching sessions with the strength of his personality.
One to one teaching makes it difficult for the teacher and student to forget about differences and move on with the course-work. The teacher and student may disagree on opinions or have major differences in personality. While this is not a real problem in a large classroom, it can stop the learning process in a one to one setting.
Students will expect teachers to customize their private teaching sessions to fit the student's specific needs. It can be difficult to continually assess the student's capability and then alter the approach and material accordingly. This gives the student a much more focused learning experience, but it demands more work on the teacher's part.
The teacher must always be "on" in a private setting. There is little time for rest during a long teaching period, unlike in a traditional ESL classroom, where an entire classroom full of students practice language drills and participate in games.
An additional pressure on the teacher is that he is expected to get the student quick results from their time together. The teacher carries considerable responsibility in a one to one setting, and is often blamed by the student or the parents for less than impressive improvements in English language skills.