Passport is a freedom tool. With second passport your options for traveling, freedom and taking care of your money multiply.
Governments control their citizens with passports. With taking it, government can limit your movement and put you under house arrest.
Obtaining second passport in most cases isn’t easy, but once it is done, it gives you freedom from single government. If you are American citizen, it is getting increasingly harder to open offshore account with U.S. passport. That alone should be enough of a reason to obtain second passport.
Having a second passport also decreases dangerous situations, where citizens of a certain countries are targeted.
Your own government can decide to take away your passport in case of felony or for almost whatever reason. This way they can limit your traveling options and freedom. Having a second passport gives control back to you, as you can use second passport to get away from the country, which imposes restrictions on your freedom of movement.
In the worst case scenario, time may come, when your country faces severe political and economical instability or even war. In such case your current passport would become pretty much worthless. With second passport however, you can move away from dangerous situations.
When you become citizen of another country, this right can pass onto your children.
Obtaining new passport will take anywhere from 3 to 10 years, depending on the country.