Question: Multiple times I've found myself in a situation in a meeting where I'm laying out my plans for a project I've been assigned and either my manager or a co-worker identify something to be impossible and therefore I should do something else (taking the time to explain how to do it). Instead of trying to convince them that my plan is possible in the meeting (which I've learned the hard way is a very bad thing to do), I instead after the meeting go and create a proof of concept to show that it is possible and present it the next time we have a meeting about my project with pros and cons compared to the solution they presented.

Is this bad etiquette on my part and should I just go with the group and implement the suggested solution just to keep a good rapport with my coworkers (not making them look bad).  

Normally if the meeting is about my co-worker's project, I won't do anything after the meeting if they choose a different path than what I would have done and if my boss or co-worker states that they don't want something implemented a particular way and they don't specify that its because they think it's impossible I respect their viewpoint and adjust my project accordingly.

If this is bad etiquette, what should I do when someone is trying to guide my project using known incorrect reasoning?

Answer: 
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> If this is bad etiquette, what should I do when someone is trying to
> guide my project using known incorrect reasoning?
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Make your case. If they reject your suggestions, ideas, and opinions then do what your boss tells you to do. It isn't your company. It isn't your decision. At the end of the day, they pay you to perform work. You may sometimes disagree with that work. That's OK.
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> I instead after the meeting go and create a proof of concept to show that it is possible and present it the next time
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Do this before the first meeting. Meeting dynamics are things to learn from. If you want something to happen a certain way you prepare for the meeting and have your strategies in place before it starts to accomplish what you want. Make this a normal part of your meeting preparations.

Anticipate objections and overwhelm them, you have the huge advantage of being prepared and ready while others are raising issues on the fly.