Objection handling is a skill you need to master. There are some books that cover this topic - Strategic Selling (by Miller and Heyman i think) comes to mind. I'm sure it has a section of objection handling. The process is the same regardless of audience - investor, prospect, business partner (biz dev), or prospective employee. You are a developer / data scientist. If i had to bet, when you are pitching to prospects or potential business partners or potential employees (not necessarily investors) you are probably pitching to other IT people, am i right? It makes sense because it's what you are comfortable with. I would suggest changing your target audience, but that's a whole separate discussion. Engineers/developers like to challenge presenters - it's just their nature (i'm a recovering engineer). It's often part of their process to see if you 'know your stuff'. They often want to be sure that you know they are the smartest one in the room. You have more in common with them than differences so try to find your commonalities and connect at some level. This goes to point #1 below - do you homework BEFORE you walk in the room.
1. Most importantly:do you homework BEFORE you walk in the room. This goes to your question about "remedies". Know your audience. That means knowing their business, their culture, their products, etc. This means knowing who the individuals are and their roles in the company and their role in this meeting - is this a product evaluation meeting, an implementation meeting, an investor meeting, etc. Will their boss be in the room? Often people want to show off for the boss and they will challenge you simply to show the boss that they know their stuff. If there is any chance they can interpret you or your product as threatening their job or turf or expertise then you need to be prepared to address that - best done so ahead of time. One way is to have a discussion about this with a manager in the group and just ask "do you think anyone will be concerned about how our product might affect their job and if so who, how, why?" etc. Always best if you can build a response that shows how your product will actually HELP them as an individual - more freedom, more responsibility, less time spent on menial tasks, safety, job security, new skills, higher pay, etc. This is a long topic, but it all comes down to understanding the process of how people and businesses decide to purchase and doing a lot of homework up front.
2. When an objection comes up: be SURE you understand the objection. Nothing worse than getting your hackles up and arguing over something YOU misinterpreted. If you are not crystal clear on what they are saying or objecting too then by all means ASK QUESTIONS until you are sure you really understand their issue. Even if you think you understand the objection, take the time to process their words the repeat the objection back to them in your own words to be sure you are both on the same page. If they have a good point, tell them so. If they are wrong don't tell them so. There are very few instances where challenging someone in real time in the room in front of others is OK, and it's always risky. Attempt it do so only if you KNOW you can win and always do so politely. The other 99% of the time there are better options. One of the most effective is to try to address the issue off-line with the person 1 on 1 - "you bring up a good point. We think we have a good solution to that, but it's a rather involved discussion. Can i get 20 minutes of your time with a white board and my laptop to unpack this issue?" After you've done enough pitches you will have ready answers to most objections. You will get to the point where you can spot objections laid by competitors. An important part of your up-front homework process is uncovering possible objections so that you have time to process them and come up with appropriate responses OR to put them to bed before the pitch. Again, long topic. happy to address in more detail offline.
3. find/build a "champion" prior to the meeting/pitch: champions are people in the audience who want you to win. They are often in a position to help you address objections, find workarounds in advance or handle the objection for you in the meeting. Definitely worth your effort to try to build this relationship before the pitch.
4. Punt: as you can see by far the best answer to this issue is to do your homework to be sure this is the right prospect to be pitching in the first place and if so then doing more homework to uncover objections and detractors ahead of the meeting. You noted that some of the people you pitch to are referrals - leverage that referral the best you can so you know the land mines before you walk in the door. If you choose not to do your homework or for some reason you can't gather the necessary intelligence prior to the meeting then:
5: Fall on your sword: never blame them. something along the lines of "I'm getting the impression that this may not be the best fit. We clearly didn't do our homework to understand your needs. we sincerely appreciate your time. ...".
6. Leverage the feedback: "you bring up some very interesting points. clearly you know this topic well. Do you have some time tomorrow/next week... to go into more details? That would be most helpful."
7. DO YOUR HOMEWORK: yes, it's that important. You will have pitches where the objections are simply misplaced. If you know their business well enough and you understand their position in the company and the decision process well enough you will find occasions where the following approach works well. Sometimes a prospect does something one way because they can't do it the right way or have never considered doing it a better way. Sometimes it's OK to tell them that they are the only ones and they could be at a competitive disadvantage. So, for example: "OK, i think i understand your objection - you mean this, correct?. OK i also understand your business and your boss told me that you currently do it this way, is that correct? OK, My understanding is that the reason you do it this way is because of this limitation and this limitation, is that correct? OK. I'm not here to tell you that you are doing this wrong, but these 10 competitors of yours do it differently (or "do it this way..." as long as you don't compromise their trust). They are able to do it differently because of our product and it gives them these advantages .....". If you have a champion in the room they will be smiling. Sorry for the long post. let me know if i can help.