Reinsurer rhymes with:
insurer, insurer, insurer, surer, durer, fuhrer, furer, insurer, juror, moorer, poorer, procurer, purer, surer
Reinsurer sounds like:
rainger, rainmaker, ramaker, ramser, ramseur, ramseyer, rancher, ranchera, ranchero, rancor, ranger, ranker, ransier, reininger, reinsure, rencher, renegar, renninger, ringer, rininger, rinker, rominger