Why do mutations occur in inbreeding?

By inbreeding, individuals are further decreasing genetic variation by increasing homozygosity in the genomes of their offspring. Thus, the likelihood of deleterious recessive alleles to pair is significantly higher in a small inbreeding population than in a larger inbreeding population.

Does inbreeding cause mutations?

According to some estimates, you and I each carry about 1 strongly deleterious hidden mutation. When homozygous, these mutations reduce fitness; inbreeding will therefore lead to inbreeding depression as the homozygous mutations become expressed. However, inbreeding isn't all bad, and many organisms habitually inbreed.