An astrologer once told me that each of the three elemental signs represents stages in our spiritual growth. For example:
Cancer - being the first water signs are more inclined to handle their emotions similar to how a child would, which include but not limited to: chatty, outbursts, talking back, emotionally reactive.
Scorpio- being the second water sign- is more inclined to handle their emotions like a teenager going through puberty. Moody, standoffish, secretly insecure but which they mask with artificial confidence or aggression.
Pisces- being the third handle their more like an adult. That doesn't mean that they are more mature than other signs, just that adult knows how to use their emotions and other peoples feelings to their advantage—hence giving them a bad reputation for being emotionally manipulative.
So why are Cancers so emotional? Well, every Cancer is different, so what makes them sensitive will be unique to the individual. Being one of the first signs in the zodiac (4th after Gemini), You can kind of look at Cancer as a young soul, where everything they see that makes them feel... demands a response, and Cancers feel everything. The fact that they are cardinal signs further propels them to act without thinking their actions through, especially in the heat of the moment.
Let's look at what Cancer represents… Home and Family Roots. Can you selfish people imagine how vulnerable you have to be to treat someone like family? Some (like Cancer) do it naturally, where Scorpio is more cautious (due to betrayal and trust issues that stem from the past) with treating people like family. When you do one little thing that annoys a Cancer, they justify their annoyance and dramatic response based on how they treated you in the past. They naively believe that if they treated you well, and looked out for you a few times, then you should be more considerate of their feelings and less annoying. However, after a shady outburst and a 40 min venting session, they'll quickly get over it.
Lastly, Cancers being so emotional is what makes them great listeners. The best listeners know how to empathize while others confine in them. Cancer may over empathize with others, especially if they are listening to another's pain.
Hopefully, you found the info beneficial, Cancers can be quite sensitive, but this is what makes them intuitive, nurturing, and supportive. Sensitivity = Empathy and you want a lot of Empathy around you when you are going through rough times.
Only Sun signs were taken into account in this response. More specific info on why a particular Cancer is emotional can be explored with the individual's Natal Chart. This will show the placements of other planets that influence spirit and the psyche.