Have you ever needed to share a taxi at an airport?
May be delays and cancellations have forced you to return to the city centre with no other means of transportation but an expensive taxi ride. Share one would be a good choice if you could find somebody going in the same direction.
Perhaps you have hit a long queue at a taxi rank after your commute flight on a Monday morning, and while waiting your turn, you could realize that most taxis were leaving with just one person.
If you could share a taxi with three or four people, the wait would be reduced by the same proportion, would save you money in travel expenses and perhaps even could do a business transaction or simply meet interesting people.
Someone with a suitcase of clothes for a week, and wearing an executive looking suit should not cause you many problems in a taxi.
Why are all these people not better organized in these taxis to optimize resources?. There may be several reasons, but surely that is because until now no means to plan such trips were available on the internet. All websites for carpooling currently available are limited to people who travel from the same origin to the same destination. At most they let you specify some intermediate points for long routes.
How likely is it that people in the same taxi to go to exactly the same place? They are small enough not to try to find fellow taxi passengers. On the other hand, it is very likely to meet someone who you could stop along your way or who could drop you off along their way.