The situation you describe is a little vague - confrontational interviews are rare - but I'll offer some assistance.
First, your frame is wrong. You are already stressed about this. You are not coming from a place of abundance. Remind yourself how your current situation is good even if you have to stretch to do this. Think of the interview as a mutual discussion and you are trying to obtain info why would or would not want to work there.
Second, focus on how you will benefit them and what value you provide. Ultimately you have to provide value to others in this life and in most situations people with sufficient insight to recognize the value you bring will eventually reward you for it; we make errors when we focus on the rewards before the value we bring. So think through how you will work with these folks, how you can bring value to their company, what makes you a better candidate than others, etc. Write these out and focus review them at least daily. You don't need to recite them in the interview but the more you internalize the value you bring the more relaxed you will be in the interview and the less supplicating you will do.
Third, do the obvious and focus on softening your presentation - body language, voice, vocabulary, etc.
Fourth, try to anticipate their objections. I recently had an interview that became a bit hostile. Reading between the lines they were concerned that I would be too prescriptive and limit their ability to make choices. I told them "my job is to identify alternatives for you as well as the pros and cons of each alternative. I'm often not in the best position to weigh those pros and cons because I won't have access to all information like you do, so obviously you will have to make the ultimate decision but I will do my best to identify alternatives and the consequence of each." They liked that approach.
Besides your aggressive demeanor, I don't know what else about you they might object to but in your mind picture a conversation where they confront you about it directly and think through your best response. I find that scripting this well before the interview allows me to brainstorm more and also to cut out things that upon reflection I might say that might be bad. Also, realize that they probably won't vocalize their objections so you need to steer the conversation to them, lay them on the table, and explain why their objection is not valid.
First, your frame is wrong. You are already stressed about this. You are not coming from a place of abundance. Remind yourself how your current situation is good even if you have to stretch to do this. Think of the interview as a mutual discussion and you are trying to obtain info why would or would not want to work there.
Second, focus on how you will benefit them and what value you provide. Ultimately you have to provide value to others in this life and in most situations people with sufficient insight to recognize the value you bring will eventually reward you for it; we make errors when we focus on the rewards before the value we bring. So think through how you will work with these folks, how you can bring value to their company, what makes you a better candidate than others, etc. Write these out and focus review them at least daily. You don't need to recite them in the interview but the more you internalize the value you bring the more relaxed you will be in the interview and the less supplicating you will do.
Third, do the obvious and focus on softening your presentation - body language, voice, vocabulary, etc.
Fourth, try to anticipate their objections. I recently had an interview that became a bit hostile. Reading between the lines they were concerned that I would be too prescriptive and limit their ability to make choices. I told them "my job is to identify alternatives for you as well as the pros and cons of each alternative. I'm often not in the best position to weigh those pros and cons because I won't have access to all information like you do, so obviously you will have to make the ultimate decision but I will do my best to identify alternatives and the consequence of each." They liked that approach.
Besides your aggressive demeanor, I don't know what else about you they might object to but in your mind picture a conversation where they confront you about it directly and think through your best response. I find that scripting this well before the interview allows me to brainstorm more and also to cut out things that upon reflection I might say that might be bad. Also, realize that they probably won't vocalize their objections so you need to steer the conversation to them, lay them on the table, and explain why their objection is not valid.