The answer to 'why is my carpet greasy' is that there are a few common causes for a greasy carpet. Spills and stains from cooking oils, lotions, or other greasy substances can leave a residue on the carpet fibers. Over-shampooing or using too much carpet cleaning solution can also lead to a greasy buildup. Additionally, if the carpet hasn't been cleaned thoroughly in a long time, dirt and oils can accumulate and give the carpet a greasy appearance.
If your carpet feels sticky or looks discolored, that's a good indication that it has a greasy buildup. The solution will depend on the cause - for minor spills or over-shampooing, you may be able to spot clean the affected areas. But if the greasiness is more widespread, you'll likely need to deep clean the entire carpet to remove the built-up residue.