Many people that hire lawyers think that whatever the lawyer does is the right thing to do. A big part of the reason why that is the case has to do with the fact that people are not educated about such matters. They assume that the lawyer has gone through a rigorous training process and as a result of the fact that this is the case they can fight your case in court in the best way possible and that nothing you say or want is going to be of much value.
The truth of the situation is that while all lawyers will have passed the bar exam this just means that they have fulfilled the bare minimum requirements to become the lawyer. This just means that they know the law enough to pass a test, not that they can apply their knowledge in a way that would be beneficial for you.
A major red flag you should be wary of when working with attorneys for personal injury in Miami is if they try to settle too soon. No good personal injury lawyer is going to want to settle when it comes to things like this. They know that the first offer is just a test to see whether or not you will take the bait. If they know what they are doing and have your best interests at heart, they would do the right thing and tell you that you can get a lot more if you want to take the case further by refusing the initial offer.
Suffice it to say that accepting the first settlement is a rookie move and you should never accept something like this.