According to academic psychological resources, the reasons are as follows:
•“Reclaim body” fantasy•“Perfect body” fantasy•Often if one is unsatisfied with results of previous
modification, might seek out changes that are more extreme or risky•S&M
There are many more reasons, but I chose the ones I thought would relate to upper class Victorian Women.
1) Victorian women would have been interested in "reclaiming" their body for themselves because they were seen as property and objects belonging to men. Tattooing offered them a way to take control of what they put on their body.
2) Obsession is an understatement when one is talking about how Victorian women treated the idea of a "perfect body." They would undergo daily pain of the corset, bustle, crinoline, etc, to look like the ideal they were bombarded with on a daily basis through magazines, advertisement, and simply conversation. The tattoo was another way to complete their perfectly trendy appearance.
3) If one could not get their waist down to the ideal 17-18 inches, one could feel dissatisfied with all the work they have done to their body. Tattooing was a sure way that their modification would be successful.
4) The entire Victorian society was based around women being submissive to men. In many accounts, women go so used to this, they even began to like it. They started to enjoy the pain caused by their corset. Many even practiced "tight-lacing" with their husband. Where he would pull the corset so tight as to restrict breathing, causing an erotic pleasure. Tattoos are synonymous with this pleasure/pain dichotomy. The pain of the tattoo makes one experience pleasure similar to that of sex or drug use.
The more I look into this topic, the less shocking this trend becomes and the more it makes sense.