Pornography can cause marriage problems, both in terms of addiction (just like gambling, alcoholism, drugs, etc) and in terms of the sexual relationship one has with their spouse (just like unwise money handling can cause problems with the financial relationship with the spouse). Pornography, like any other fantasy material, can engender unhealthy expectations and can give poor lessons on what human sexuality is and can be. Some women compare themselves and their sexual relationship with the actors in pornographic material and feel inadequate in many ways, and that can hurt intimacy.
Some religious leaders have found that some percentage of men are susceptible to significant addiction, or that some statistically significant number of women will not be able to have a strong relationship with someone who consumes pornography.
This doesn't mean that everyone will suffer these problems, nor that marriages are falling apart right and left due only to pornography.
Of course they would advise their church members that consuming pornography has some risk of hurting their marriage. Just like getting an immunization may prevent a one in one thousand chance of getting a fatal illness, staying away from pornography may prevent a one in one thousand chance of damaging their marriage.
Also, this probably should have been posted in the politics/religion subforum...