The Supreme Court is wrong on this point. In Henderson, the court distinguished between appeals to an Article III court (as in immigration cases) and appeals to an Article I court (as in veterans benefits). The Supreme Court did not explain this distinction.
It did look to the language of 38 U. S. C. §7266(a), the statute allowing Veterans appeals, and said that language is not "jurisdictional."
We see no distinction between this language and that allowing appeal in immigration cases. INA 242(a)(2)(B) says an immigration appeal "must be filed not later than 30 days after the final order of removal." If the court sees a distinction between the words "must" and "shall," it did not explain the difference.
“In order to obtain review by the Court of Appeals
for Veterans Claims of a final decision of the Board
of Veterans’ Appeals, a person adversely affected by
such decision shall file a notice of appeal with the
Court within 120 days after the date on which notice
of the decision is mailed pursuant to section 7104(e) of
The Supreme Court also noted that 38 U. S. C. §7266(a) does not include the deadline in the section titled "organization and jurisdiction" but rather under the "procedure" section of the statute. INA 242 does the same thing, placing the deadline in 242(b) under the heading "requirements for review of orders of removal" instead of in 242(e), which has the heading "exclusive jurisdiction."
The court also found significant that in Veterans appeals, the administrative Board can review the denial of benefits de novo and, and a veteran can reopen her denied appeal with new and material evidence. Immigration appeals have the same form, and there is little or no distinction here. Without better explanation from the court, we are left to wonder why it is that veterans appeals are not jurisdictional but immigrant appeals are - given the similarity in statutory language and scheme in both cases.