Your error isn't the result of an inept parsing of the text. Your error is indicative of someone attempting to make a text say one thing, when the text actually says something else. You, and other Catholic apologist begin with the answer you want to hear, and twist the scripture to support your preconceived conclusion. Your religion has a so-called "oral tradition" it invented. The claim is made that particular ideas were not located in the written word, but were passed down verbally. But some how, after all these years, the oral tradition is still known, even when no written record of it exists. Or, if a written record exists, it is NO LONGER ORAL tradition is it?
This is the oldest con in the world. Suppose a man claimed to have black boxes that answer every question truthfully. He sells them at a hefty price. Suppose another man wanted to test it before buying. He asks it, "what is the day of my birth?" Once the answer is printed out on paper, it is totally incomprehensible. The first man tells him, "I am the only person who can interpret the message."
This is Catholic Oral Tradition in a nutshell. Not only do Catholics claim to have apostolic messages from the third century, they reserve the interpretation of those messages to themselves. As I said, the oldest con in the world. A claim that can't be tested is a dubious claim.
Catholic apologists are con men, attempting to fool the gullible, who don't understand the dangers of proof-texting. Those who take a verse out of context can make it say whatever they want to hear, or whatever they want to argue. Does Paul talk about traditions that he communicated orally? Yes he does. Do we have an infallible source for some of these traditions? Yes, the written scriptures.
Should we accept the word of other men who claim to know about other traditions? No. Our only source of information regarding divine revelation is the inerrant, infallible, inspired scriptures. If Paul verbally gave other traditions, which cannot be found in the Bible, they are lost to history.