Yossii—You are not mechuyav to die rather than embarrass someone. The Loshon of the gemara is “נוח לו לאדם”-it is appropriate for a person etc
The Rambam on embarrassing another (דעות, ו, ח) (translation from chabad.org)
“At first, a person who admonishes a colleague should not speak to him harshly until he becomes embarrassed as [Leviticus 19:17] states: “[You should]… not bear a sin because of him.” This is what our Sages said: Should you rebuke him to the point that his face changes [color]? The Torah states: “[You should]… not bear a sin because of him.”
From this, [we learn that] it is forbidden for a person to embarrass a [fellow] Jew. How much more so [is it forbidden to embarrass him] in public. Even though a person who embarrasses a colleague is not [liable for] lashes on account of him, it is a great sin. Our Sages said: “A person who embarrasses a colleague in public does not have a share in the world to come.”