Just to point out… the rule there says the GM may offer Determination, which, therefore, might be read as optional.
I definitely think the GM should be doing it, as that’s obviously the intent and a key aspect of gameplay, but they may have read the rules and decided against it because of that pesky word may implying that it’s the GM’s choice and not a hard and fast requirement.
Yes, it – of course! – is optional. But “it” in this respect comprises the whole package of Determination and Complication and not only the point of Determination. The GM has a (free) choice, but it’s not the choice “do they get Determination or not?” but “do they get Determination in exchange for a Complication?”.
The idea behind this rule is an incentive for the players to stay within character through player empowerment. Which is great, by the way.
Let’s say there’s a Chief of Security with a Value called “Proud Daugther of Andoria” who is accompanying their CO on a diplomatic mission. The other side is represented by a Vulcan who acts arrogant and a bit provoking. This is the situation where the GM could say: “Hey, Commander Zharath, this Vulcan is really annoying you. You could keep your composure and nothing will happen, or you could be a Proud Daughter of Andoria and confront him. In this case, you will earn a point of Determination for sticking to your Value, but I will set the complication ‘annoyed by Zharath’ on the Vulcan, raising the Complication Range for all social interaction with him by one, as long as you’re present.” The GM is not obligated to offer Determination/Complication. But without Determination, there will not be a complication related to the Value.
Of course, the GM could set the very same Complication with the very same NPC – but not, because Zharath is a “Proud Daughter of Andoria”, but, because he just doesn’t like Andorians himself. The difference is that this is completely unrelated to the player’s Value(s).
The point I’m trying to make is that sticking to a Value is a player action. The GM can not force a PC to act in a specific way. Player agency is the point of RPGs. Thus, the GM can not set a complication for a an action they just forced the PC to do. What they can do is offering a point of Determination for a specific PC action that would make the situation more complicated or more difficult.
Well, I took a look a you tube and… I can’t remember the adventure! But there are several adventures that use Determination up to and including challenging it and the changing of it at the end.
I just looked up Star Trek Adventures and had a plethora of hits, sit back and watch a few of them.
Also, have you been using the point of Determination you get in the beginning? Seeing it being used could inspire your GM. It could be that he is just not confident in using it rather than trying to keep something from the characters.
Yes the point in the beginning has been being used but no chances to earn it back after use currently
Did your GM explain any reason why they don’t want to use the Determination mechanic? Maybe they have a good point…? 
His 1st reason was that the totorial on you tube did not do it. Currently it is that it is too over powered for the players. It is the GMs choice. But when going over the game mechanics it seems like a major missing component to not be using it. It is what gives the game some of what makes the show so great. Just because a persons character is not a engineer, a doctor or even a commander does not mean that for a breif period they should not be able to focus their attention to accomplish a small task outside of their feild in a pinch. But that is my feeling of it. I post here to see how others are using it and how they feel it works in game play. Especially when the common GM complaint is to stay in character.
It is a major missing component to ignore. You say “it’s the GMs choice” but remember that who GMs is the group’s choice. It sounds to me like it’s high time to reevaluate who fills that role.
Next complaint like that from the GM, respond with ‘You aren’t letting me.’
Determination and utilizing values in a negative way is part of what makes your character who they are.
Similar to roles: If your character is a Chief Engineer, they get the engineering team as an advantage. Your character, as the chief engineer should be able to decide how that team is utilized and suggest ways for that advantage to come into play. Having the GM determine it for you takes away part of your character.
For values, I have a character currently with a value of ‘Unknown and Invisible’. He gets into a lot of shenanigans keeping to the mindset that he is still unknown and invisible, even though he is not. This will eventually (hopefully) lead to a situation where I can activate it in a negative way on more than one occasion. The first time I would gain the determination and a complication based off of the situation and the value. The second time is when I would like to challenge that value to replace it.