Do you want an alternative point of view that you can use to challenge your negative thoughts? I don't intend for this to cause you upset or distress, I just see your work issues from a coworker/employer perspective which is different from your perspective. If you want to challenge your negative thoughts, you must change your perception instead of indulging your negative point of view with avoidance and self sabotaging ideas.

Is it possible that the coworker who asked about sitting in his client meeting was trying to help you find new inspiration so you can get through your current task? Is it possible that this person sees you struggling and offered you help? I think you missed a good opportunity to learn from both a client and a coworker. If that coworker has been successful at your company, wouldn't they be a good resource to learn from? Actions speak louder than words. You asking for help (even in your own thoughts) and then declining the help that's offered suggests you don't want help and want to struggle. I've seen this before in highly intelligent and capable coworkers. One person declined a small olive branch from one of the best mentors in the company we worked for and it turned out to be a career ending move.

Is it possible that your employer is keeping you employed because they believe in you? You seem so convinced that your employer can't possibly find any value in you or any reason other than your negative perspective to keep you employed there. From my point of view, they could be keeping you because they do value you but you can't see it and are even fighting against being valued. Saying your tasks are menial devalues any effort you put into it. Your employer isn't saying it's menial... you are. You can't simultaneously be too good for this menial task and not good enough to complete it. Pick one.

Avoiding meetings because you are afraid to say that you have no idea what's new and exciting in your field means you missed a chance to be inspired by others and what they think is new and interesting. These meetings aren't just a test of what you know, they are meant to be a jumping point for new ideas. You could have said in that meeting, I've been so focused on one task, I've missed out on some new things. Thanks for sharing what's new or I'm looking forward to hearing about what's new or hmm that's interesting, I'll have to look into that more. You bailed on being an active participant. If you want to be successful, you need to participate. The way you've been participating hasn't brought you the result you want, so try a new way.

One last thought... you mentioned something about others not understanding how hard it is to keep doing the same task over and over... I get that you don't like this particular task you are doing and you're complaining to vent your frustration. The monotony of a repetitive task can be disrupted by attending a coworkers meeting, going to a team meeting... use the opportunities that are presented to you to get a change of mental pace at work. My boss used to schedule short safety meetings in the middle of our end of month crush of monotonous computer based tasks and crazy boring budget reporting. People complained like you wouldn't believe. I suggested he change the name to "monotony busting safety breaks". Attendance and productivity up, complaints down. What do you have to lose by challenging your negative thought patterns?