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I am currently investigating some generalized properties in my mathematical research with my professor. We are basically now working together to produce new paper to publish.
My professor is very well experienced and he seems to know what he is doing very fast compared to me. I feel like I do not do anything worth the contribution for this project.

Is it normal for a first year master student to feel this way when he or she tries to write a paper together with a professor? How come can a person generate possible ideas to solve so fast? Is it because I am still inexperienced or am I doing something wrong?

I usually read some papers trying to get some ideas which might be useful but I still dont get anything really 'valuable' for the progress of my current project.

I am hoping for some advises coming from well experienced mathematicians / researchers. Thank you very much!

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It seems to me that you are looking more for reassurance than advice. There's absolutely nothing wrong in seeking that on an online forum, but you must first speak to your professor and senior students working in the group. The internet is comfortable in anonymity, but you must not develop an aversion to asking people for help in person. That may be far more harmful than being stuck on a research project.

Now, remember you are at the very beginning of a research career. Your professor has spent years and years. Isn't it unreasonable to expect yourself to generate ideas at the same pace? To answer your question, there is certainly an inexperience component. Whether you are doing something wrong can only be ascertained by your professor. Most likely, you are worrying needlessly. There is, however, always a chance that this line may not be ideal for you- you will have a better idea of that by time your program ends. Your professor will be invaluable here too, but you need to take the first step and open up to him.

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    Thank you very much for your advice, my professor says it is okay to fail as long as I can realize where I fail and try not to repeat the same failure as a lesson. – Evan William Chandra May 24 '18 at 4:34
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Your post makes me think of the woman who always does the laundry because, as she puts it, "It would be so much trouble to teach my spouse how to use the washing machine, I might as well just do the laundry myself."

Ideally, an advisor will distinguish between a paper that needs to get out the door quickly, and a paper that is a suitable project for a Master's student, who may progress more slowly than the professor working alone would.

You might want to try gently asserting yourself with your advisor, e.g.

I feel frustrated when all I do is watch you do the work, without making any contributions myself. I feel like I need to work on a project that you don't need completed super quick, so that you'll have time to give me suggestions of directions to go, and then be able to sit back and patiently allow me to see how far I can get at each step, before you jump in and just show me that step, already worked out.

A side thing that might help you would be to form a study group with some fellow students. Working out problems together, and discussing a particular journal article after everyone has read it, may help you develop your skills, and increase your self-confidence and self esteem.

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