The section you are refering to, including an extract from the poem that Anne received from her father on her birthday, was written on Sunday, 13th June, 1943. Anne does not quote all the poem, but the bit that she does includes interesting references to her father's understanding of Anne's position and her sense of frustration, and also asks for her understanding as he and her mother try to do their best to bring her up in such difficult conditions:
Please bear with us, your parents, for we try
To judge you fairly and with sympaty.
Correction sometimes take against your will,
Though it's like swallowing a bitter pill,
Which must be done if we're to keep the peace...
This is a very endearing comment from her father, and points towards the way that he knows they have made mistakes as parents and also how difficult it can be to receive "correction" as a child. The poem also pokes gentle fun at the situation with everybody desperate to be part of Anne's education and the kind of moans that she has. Lastly, it establishes the love that her father feels for her, and how proud he is that she is a girl who "brings us all fresh air" and never stops studying. He recognises that she could have "lived in such a different way" and is proud of the way that she is coping with the situation.