There are two causes of inbreeding: inbreeding due to genetic drift and inbreeding due to non-random mating. Or in other words: inbreeding due to coincidence and inbreeding on purpose, inevitable and evitable inbreeding.
Genetic drift causes a loss in genetic diversity due to loss of alleles, which leads to an increase in homozygosity and this is also called inevitable inbreeding. Imagine that at some moment in history a mutation occurred. You may assume that this mutation only occurred in a single animal, as it is unlikely that exactly the same mutation also occurred in another animal. Animals that carry the allele today, therefore, must be related because they have that original animal as common ancestor. This is the case for all mutations, even if the animal in which the mutation occurred lived a VERY long time ago. Given the definition that inbreeding is the result of mating related individuals, animals that are homozygous for the allele must be inbred. Homozygosity in a population is an indication of size of allele frequencies. If all animals are homozygous, the other allele(s) is/are lost from the population. Inbreeding due to genetic drift results in a permanent loss of genetic diversity because alleles are lost for ever.
Non-random mating can cause inbreeding, but this is evitable. Mating closely related animals on purpose, like brother and sister or father and daughter matings, results in an increased probability that the offspring of the mating will receive the same allele from both parents. This results in increased homozygosity, and thus in inbreeding. However, this is a temporary loss of genetic diversity because if you would stop mating closely related animals on purpose, but use random mating instead, this cause of inbreeding would disappear.