INTROSPECTION - when you offer to take someone home after a first date and they refuse

IF they refuse straight forward or politely, it may not be your problem. It may be that they don't feel worthy enough, they might test you (especially women do), they might expect you to beg / ask them a few more times for confirmation (to see whether you are needy or not), they don't like you or maybe they are happy they took advantage of the situation and you're discardable now (worst case scenario). They might be suspicious of your intentions, they don't want you to know where they live / what their house looks like, or whether they have someone else already (whom they might be in an abusive relationship with and they don't want you to worry about them).

These are all introspection-based ideas and are obviously all possibilities. One needs responsibility in their actions and in learning about people they interact with (and most importantly their pains). Whichever of these cases, and whether they DO accept to be taken home - well, one needs to take their time. Impulses can help in life, but will only take one to their misery sooner or later.