I will give you the basics, but I would also suggest checking out this thread: http://forum.bioware...confrontations/
For the loyalty confrontations between Jack/Miranda, and Tali/Legion, it is easier to pass the Jack/Miranda persuade check with the renegade option, and the Tali/Legion persuade check with the paragon option. My guess is you are playing a mostly paragon game and therefore are finding it difficult to pass the Jack/Miranda persuade check.
How does the persuade system work? Every time you go on a mission, or go to a new area like the Citadel or Omega, there are a certain number of morality points available that can be earned. Let's say you visit Omega. You can talk with Aria and earn morality points. You can talk with the Batarian bartender and earn morality points. You can talk with Kenn and earn morality points. Etc. Add all of these different opportunities together and you come up with the total number of morality points you could earn in this area you just visited.
For the Omega example, let's say there were 200 paragon points possible to earn and 150 renegade points possible to earn. Omega is your first port of call, you have not visited anywhere else or done any missions. When you visit you talk to some people, but not everyone (maybe you didn't realize they were there). Through your dialogue choices you earn 125 paragon points, 25 renegade points, and you were neutral on some responses and so didn't earn some 25 morality points when you could have. You also forgot to talk to two people (say Captain Gavorn and the Batarian bartender) and so missed out on earning another 25 morality points.
Your paragon percentage in the above example is 62.5% (you earned 125 paragon points out of a possible 200), and your renegade percentage is 16.666% (25 out of 150 possible).
When you get to a persuade check the game makes each persuade check require a certain percent to pass it with a paragon option, and a certain percent with with the renegade option. Let's take the Jack/Miranda dispute and use some make up numbers as an example. It is easier to pass this persuade check with the renegade option than with the paragon option. So let's say the renegade percent needed is 30% and the paragon percent needed is 80%. Since your paragon percent is 62.5% and you renegade percent is 16.666%, you will not be able to pass this persuade check with either option. If, instead you had earned 160 paragon points, you paragon percentage would have been 80% and you could have passed the persuade check.
So, the first thing you need to know is that the game is trying to force you to be all paragon, all the time, or all renegade, all the time.
Second, if you use an import from Mass Effect 1, you can import up to 190 paragon points, and 190 renegade points.
Let's use an example where you imported 190 paragon points, and 100 renegade points and made all the same dialogue choices as above. In that case, you would have 125+190=315 paragon points, and 25+100=125 renegade points. Your paragon percent is 157.5%, and your renegade percent is 83.333%. Since 157.5% is greater than the 80% needed to pass that paragon level needed you will have that option available. And, since 83.333% is greater than 30% needed, you will also have the renegade option available.
Therefore: it is considerably easier to pass persuade checks if 1) you import a lot of morality points from Mass Effect 1, and 2) if you get to the difficult persuade checks early. The second point is because as you open up each new area and run each new mission, the total number of paragon and renegade points available keeps growing, while you may miss some of them, and so your percentage of the possible score keeps decreasing.
So, for the Jack/Miranda dispute, if you wish to pass it with the paragon option, are: 1) import a lot of paragon points from ME1, 2) do both Jack's and Miranda's missions as soon as they are available, 3) make sure you are not skipping out on opportunities to earn morality points (missing people to talk to, including the crew or going neutral), and 4) always pick the paragon option when talking to people.
This advice is overstating things somewhat. I am often able to get both the paragon and renegade options in the Jack/Miranda dispute because most of my Shepard's are about 50/50 paragon/renegade. But I make sure I am importing the maximum number of morality points from ME1 (both paragon and renegade).
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Suicide Mission is the main goal of the game. Make good choices and everyone will survive 
