Petitioner Zhou Yi Ni, a native and citizen of the People’s Republic of China (“China”), petitions this Court for review of an October 28, 2002 order of the Board of Immigration Appeals (“BIA”) affirming a November 23, 1999 decision by an immigration judge (“IJ”) that denied petitioner’s application for asylum and withholding of removal. Petitioner also appeals the BIA’s denial of a remand for consideration of his claims under the Convention Against Torture (“CAT”), adopted Dec. 10, 1984, S. Treaty Doc. No. 100-20 (1988), 1465 U.N.T.S. 85; 8 C.F.R. § 208.16.
We begin by addressing petitioner’s application for asylum and withholding of removal. Where, as here, the BIA summarily affirmed the IJ’s decision to deny asylum, we review the IJ’s decision rather than the BIA’s order. See Zhang v. DOJ, 362 F.3d 155, 158-59 (2d Cir.2004).
Petitioner’s asylum claim rests on the persecution he allegedly suffered for violating China’s coercive family planning policy. In particular, petitioner testified that his wife was involuntarily sterilized by China’s authorities after the birth of the couple’s second child. Petitioner further claimed that, upon return to China, he would be persecuted for having fathered two children.
The IJ found petitioner not credible, based in part on serious contradictions between petitioner’s account of his wife’s sterilization and his wife’s own asylum application. The IJ also found that petitioner had not established that he had himself suffered past persecution or that he had a well-founded fear of future persecution.
Our review of the IJ’s credibility findings is highly deferential, see Zhang v. INS, 386 F.3d 66, 73-74 (2d Cir.2004), and the IJ’s “administrative findings of fact are conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary,” 8 U.S.C. § 1252(b)(4)(B); see also Chen v. INS, 344 F.3d 272, 275 (2d Cir.2003). ‘Where the IJ’s adverse credibility finding is based on specific examples in the record of inconsistent statements by the asylum applicant about matters material to his claim of persecution, or on contradictory evidence or inherently improbable testimony regarding such matters, a reviewing court will generally not be able to conclude that a reasonable adjudicator was compelled to find otherwise.” Zhang, 386 F.3d at 74 (citations and internal quotation marks omitted). A “ ‘legitimate nexus’ ” must, however, “exist[ ] between petitioner’s claim of persecution and the omission giving rise to the IJ’s adverse credibility finding.” Dong v. Ashcroft, 406 F.3d 110, 112 (2d Cir.2005) (quoting Secaida-Rosales v. INS, 331 F.3d 297, 307 (2d Cir.2003)).
In this case, the IJ’s adverse credibility finding was based, inter alia, on a specific example of contradictory evidence that undermined the very “crux” of petitioner’s asylum application. Petitioner testified that his wife was involuntarily sterilized after the birth of the couple’s second child. By contrast, petitioner’s wife omitted from her own asylum application any mention of having undergone involuntary sterilization; indeed, she submitted an affidavit stating that she left China in order to avoid sterilization. This discrepancy is, standing alone, significant enough to support an adverse credibility finding; we need not, therefore, recount the other inconsistencies identified by the IJ.1
*175Petitioner also argues that the IJ erroneously denied his claim of well-founded fear of future persecution. Because petitioner did not raise this argument before the BIA, it is not properly exhausted, see 8 U.S.C. § 1252(d)(1), and we need not consider it.
We therefore decline to disturb the Id’s decision denying petitioner asylum. An applicant who, like petitioner, fails to establish his eligibility for asylum is necessarily unable to establish his eligibility for withholding of removal. See Abankwah v. INS, 185 F.3d 18, 22 (2d Cir.1999).
Although petitioner did not seek relief under the CAT before the IJ, he did so before the BIA, and he now appeals the BIA’s denial of a remand. We review the BIA’s decision not to remand for abuse of discretion, see INS v. Abudu, 485 U.S. 94, 99 n.3, 108 S.Ct. 904, 99 L.Ed.2d 90 (1988), and we find none. Although petitioner submitted to the BIA several reports about general country conditions and human rights abuses in China, he has neither demonstrated that this information was previously unavailable, see 8 C.F.R. 1003.2(c) (“A motion to reopen proceedings shall not be granted unless it appears to the Board that evidence sought to be offered ... was not available and could not have been discovered or presented at the former hearing .... ”), nor established a prima facie case for relief under the CAT, see, e.g., Wang v. Ashcroft, 320 F.3d 130, 144 (2d Cir.2003) (holding that “ ‘country conditions’ documents” that “indicate that some prisoners in China have been tortured” are insufficient for relief under the CAT when a petitioner has not “established that someone in his particular alleged circumstances is more likely than not to be tortured if imprisoned in China” (emphasis omitted)).
We have considered all of petitioner’s arguments and found each of them to be without merit. Accordingly, the petition is denied.