This is a question I am often asked as I now reside in Denver. In fact, prior to moving to Colorado (wife's home state) I lived in Dallas-Fort Worth, Texas for most of my life. My short time in Independence, MO was from 1981-1985.
We lived less than a mile from the stadium. I remember hearing the crowd roar from our house on game day. However, at the time in my life football took a backseat to baseball. I mean, the Royals won the World Series in '85! I had a Brett Saberhagen beach towel and listened to games on the radio whenever possible.
After our move to DFW, the Cowboys eventually started becoming a good team at the same time as the Chiefs. During school recess my classmates would choose their football idols (mostly Cowboys players) as their moniker for our pickup football games. The obsession with the Cowboys was nauseating (particularly among grown adults). There were many reasons I had for not liking the Cowboys:
1) The automatic Thanksgiving Day game each year.
2) Being dubbed "America's Team"
3) I was not a fan of Troy Aikman
4) I didn't like football played in a dome stadium
So I decided to follow the Chiefs. Back then it was difficult because the hometown team was in the NFC so KC games were rarely televised. There was no Redzone, NFL Ticket, and the internet wasn't a big thing back then. Fortunately, the Chiefs had Derrick Thomas. He became the Chiefs' ambassador to relevance around the rest of the NFL. This is why I would choose him as my moniker for our pickup football games. All of my friends knew who he was.
When I graduated high school I decided to go to college in Lincoln, Nebraska. Having the Chiefs' games televised was not a deciding factor but a nice perk. However, I was crushed in college when Derrick Thomas passed away. But by this time I was hooked. I couldn't ignore the team no matter how infuriating or heartbreaking the game or season.
Next came fantasy football. Around the time I started getting involved in a fantasy football league was around the time that Dick Vermeil came to KC. I was a homer and drafted a large quantity of Chiefs players. Fortunately, a relatively unknown (at the time) running back by the name of Priest Holmes saved my season. By the time Priest was dominating football I was attending college in Washington back when Seattle was still part of the AFC West. So I had the opportunity to attend some Chiefs-Seahawks games and see Priest Holmes in person. Of course the tide eventually turned and the Chiefs became a wasteland in terms of fantasy football stars. I have since curtailed my addiction to fantasy football to spend more time with family and to actually enjoy watching football more.
After college, I moved to Denver. Many people took offense to my Chiefs apparel and couldn't understand why I didn't want to support the hometown team. There were many seasons of suffering as Denver (particularly during the Manning years) got the best of KC. I am hopeful that the Chiefs will establish some level of dominance within the AFC West for the foreseeable future.
So I guess if I had to boil it down to a single reason it would be #58.