I suggest the teacher's comment that tutoring doesn't matter is in relationship to whether or not tutoring will matter in making the decision to retain her in second grade. Of course it matters when viewed as a help to your daughter.
If you're focused on self esteem, I suggest it's a draw. Either choice could affect her self esteem. How much her self esteem is affected depends on how the choice is presented to her ( being positive) and how much educational support is given. Two of my grandchildren have IEPs based in part on their ADHD symptoms.
My granddaughter had difficulty reading because she had trouble comprehending the meaning of the text. Extra support made a difference. I suggest tutoring is one piece of support. My granddaughter often worked one on one at school. She received help at school in math and reading.
Years ago I was a school volunteer. I supervised a middle school student while he, in a room by himself, was helped by being able to take longer to finish the test and he could ask me questions.
One of my friends, as a volunteer, tutors first and second graders in reading. She treats her job as if she was paid. She worked to learn skills so she could improve her tutoring.
So, if your daughter doesn't have a 504 or an IEP, I suggest you consider getting her evaluated to see if she's eligible for one. There is a Federal law that requires school districts to evaluate and provide help to those having educational difficulty because of conditions related to learning disabilities.
I suggest you mostly listen to the principal. Ask why she is considered for retention. The answer is more complicated than she's behind in reading. Ask how retaining or not she will benefit her. Start with an open mind. Talk about reasons you want her to move to third grade. Listen to his answers before making your final decision.
I suggest that you make an appointment with the office that diagnoses learning difficulties and provides support to ask about retaining or moving forward. They see the results of both decisions in actual students. In my school district it's in the Special Education office that works with all schools.They may give you additional information based on their education and experience with students in all the district schools.