Take Anil, who reads the Gita with a pencil. In chapter 5 he underlines that the yoga of action is better. In chapter 6 he underlines that the devotee is the highest of yogis. In chapter 12 he underlines that those who fix the mind on the Lord are the most perfect. Then he puts the pencil down. Either the book contradicts itself, he thinks, or only one path is right and the rest are second-class.
This is the misreading in its plain form: the Gita names a different winner in each chapter, so its praises cannot all be true together.
Why people read it this way
The praises do sound like rival claims. The Lord says the yoga of action is better than giving up action (Gita 5.2). He says the yogi is higher than the ascetic, the scholar and the ritualist (Gita 6.46). He calls the devotee who worships Him with faith the most united of all yogis (Gita 6.47), and in chapter 12 the most perfect (Gita 12.2). Put in one list, they seem to name four winners.
What the Gita says
The Lord removes the contest in the same chapter where it begins. Only the immature call knowledge and action separate (Gita 5.4).
एकं सांख्यं च योगं च यः पश्यति स पश्यति ॥ ५.५ ॥
The supreme state attained through Jñāna Yoga is also reached through Karma Yoga. One who understands that these two paths ultimately lead to the same destination is the one who truly sees reality as it is.
The place reached through knowledge is reached through action too, and the one who sees the two as one sees truly (Gita 5.5).
Now look at who is compared in each praise. The first compares two ways for a person who is still at work (Gita 5.2). The second compares a yogi with people who practise only a part of the path (Gita 6.46). The third compares two kinds of seekers, and the verses that follow add that those who worship the unmanifest reach the Lord too (Gita 12.3, Gita 12.4). Each verse answers its own question.
A better reading
The Gita does not rank the paths against each other. It answers "best for whom, and by what measure?" and says that the paths reach one goal. Anil's four underlines do not clash. They sit side by side.
When you meet the praise of a path, ask two things: who is being compared, and by what measure?
Where to go next
The full table of comparisons is in Who Is "Best" in the Gita? Reading the Basis of Each Comparison. For the whole picture, see The Paths: Action, Knowledge, Devotion and its simple reading. For the two ways that the fifth chapter compares, see Renunciation or Karma Yoga?.