False in its first half, true in its second — so the statement as a whole is false.
Leela tells Shruti the opposite: “Your own father, Shruti, had to go against his family’s wishes to play the violin. His was a family of vocalists. Your grandfather, his father, and your uncles were all vocalists belonging to a highly traditional school.” Nabin did not follow the family tradition; he broke it, and “Your grandfather saw this choice as a kind of betrayal of family values and tradition.”
The second half is accurate — “your father worked his fingers to the bone and see where the violin got him” — but a statement is true only if all of it is true.
Why this fact is the hinge of the play: it makes Nabin’s objection to Shruti an exact repetition of his own father’s objection to him. He is playing his father’s part without noticing, which is why Leela can change his mind simply by reminding him: “I had forgotten my own past.” The chapter’s theme of tradition versus new forms is not stated as a lesson — it is built into the family’s history and repeated one generation later.