Reading for Yourself is a Way to Create a Close, Personal Relationship with the Tarot.
From what I understand of these questions and opinions, the idea isn't that a tarot reader cannot pull a daily card reading for themselves and read it but as to whether or not they could read for themselves objectively when the reading is in-depth or dealing with emotional matters in their lives.
Reading when you're emotional is one of the biggest problems when reading for yourself. My advice for this is to step back from the situation, breathe, and obtain a measure of calm.
Like a large, heavy meal, sometimes deep readings on difficult or emotional matters need time to digest.
A great way to process your thoughts, feelings, disagreements or synchronicities in and around a reading is through a tarot journal.
Instead of pulling "clarifiers" or dealing new spreads to seek out a different outcome to the situation, another way to learn more from a reading is to take a good hard look at the initial reading and what it is about the cards that you are uncomfortable with or disprove of. Write it down if you like and process the emotions you are feeling on paper. Sometimes the written word is a better clarifier than pulling a new card.
Other Ways of Pulling the Cards
The more cards you pull and more positions you have, the more chances you have to create bias or disagreements with the tarot.
You can't always get what you want. Pulling multiple cards, dealing multiple spreads, or looking up different card meanings until you get the reading you want doesn't change the situation in the reality.
If you do want to clarify the reading, try a layout expansion. I discuss a Celtic Cross Expansion in this month's Tea&Tarot. Here, we take a card from our initial reading and build another layout around it to clarify the time, action, or reason for everything happening.
Another option is the rearrange the reading. If you are pulling cards and the reading is a negative or uncomfortable one, consider what cards and positions are the culprits. Then make a conscious decision to move these cards or turn them around if they are reversed. As you do this, think about what actions you can take in your life to make this change or transition happen. The act of moving the card around is a symbolic representation of the act you intend to make to change your life. You are the creator of your reality and life so it is up to you to change things that make you unhappy. You can do this.