why say "take" when we really mean "leave" (a piss, etc.)

The use of “take” in colloquial expressions of urination and defecation continues to both confound and amuse even the youngest of language enthusiasts. Just ask my son, who will insist with a smile that he leaves a pee, piss, dump, crap, and so on, not takes one.

Below are all the meanings and senses of “take” as a transitive verb, according to the Free Dictionary (which provides one of the lengthiest lists). I’ve bolded the ones that seem to come closest to the meaning as used in the expression at hand (ahem). Of course, the expression seems entirely contrary to definitions 1 and 5.

Do any of these truly apply, or did the expression take a + product of urination / defectation somehow develop otherwise?

1. To get into one’s hands, control, or possession, especially:
   a. To grasp or grip: take your partner’s hand.
   b. To capture physically; seize: take an enemy fortress.
   c. To seize with authority or legal right: The town took the land by eminent domain.
   d. To get possession of (fish or game, for example) by capturing or killing.
   e. Sports To catch or receive (a ball or puck): The player took the pass on the fly.
   f. Sports & Games To acquire in a game or competition; win: took the crown in horse racing.
   g. Sports & Games To defeat: Our team took the visitors three to one.
   h. To engage in sex with.

2. To remove or cause to be absent, especially:
   a. To remove with the hands or an instrument: I took the dishes from the sink. The dentist took two molars.
   b. To cause to die; kill or destroy: The blight took these tomatoes.
   c. To subtract: If you take 10 from 30, you get 20.
   d. To exact: The storm took its toll.

3. To affect in a strong or sudden manner as if by capturing, as:
   a. To deal a blow to; strike or hit: The boxer took his opponent a sharp jab to the ribs.
   b. To delight or captivate: She was taken by the puppy.
   c. To catch or affect with a particular action: Your remark took me by surprise.

4. a. To carry in one’s possession: Don’t forget to take your umbrella. See Usage Note at bring.
   b. To convey by transportation: This bus will take you to Dallas.
   c. To lead or cause to go along to another place: The guide took us to the waterfall.
   d. To be as a path or course for; provide a way for: The trail takes you to the lake.

5. To receive into or on the body, as:
   a. To put (food or drink, for example) into the body; eat or drink: took a little soup for dinner.
   b. To draw in; inhale: took a deep breath.
   c. To expose one’s body to (healthful or pleasurable treatment, for example): take the sun; take the waters at a spa.

6. To make use of or select for use, as:
   a. To move into or assume occupancy of: She took a seat by the fireplace. The team took the field.
   b. To choose for one’s own use; avail oneself of the use of: We took a room in the cheaper hotel.
   c. To require the use of (something): It takes money to live in this town. This camera takes 35-millimeter film.
   d. To use or require (time): It only takes a few minutes to wash the car.
   e. To use (something) as a means of conveyance or transportation: take a train to Pittsburgh.
   f. To use (something) as a means of safety or refuge: take shelter from the storm.
   g. To choose and then adopt (a particular route or direction) while on foot or while operating a vehicle: Take a right at the next corner. I downshifted to take the corner.

7. a. To undertake, make, or perform: take a walk; take a decision.
   b. To perceive or become aware of by one of the senses: took a quick look at the sky; took a smell of the spices.
   c. To commit and apply oneself to the study of: take art lessons; take Spanish.
   d. To study for with success: took a degree in law.

8. To accept, receive, or assume, as:
   a. To accept (something owed, offered, or given) either reluctantly or willingly: take a bribe.
   b. To allow to come in; give access or admission to; admit: The boat took a lot of water but remained afloat.
   c. To provide room for; accommodate: We can’t take more than 100 guests.
   d. To become saturated or impregnated with (dye, for example).
   e. To submit to (something inflicted); undergo or suffer: didn’t take his punishment well.
   f. To put up with; endure or tolerate: I’ve had about all I can take from them.
   g. To receive into a particular relation or association, as into one’s care or keeping: They plan to take a new partner into the firm. We took the dog for a week.
   h. To assume for oneself: take all the credit.
   i. To agree to undertake or engage in (a task or duty, for example): She took the position of chair of the committee.
   j. Baseball To refrain from swinging at (a pitched ball).
   k. To be affected with; catch: The child took the flu.
   l. To be hit or penetrated by: took a lot of punches; took a bullet in the leg.
   m. To withstand: The dam took the heavy flood waters.
   n. To require or have as a fitting or proper accompaniment: Transitive verbs take a direct object.

9. a. To accept as true; believe: I’ll take your word that he’s telling the truth.
   b. To impose upon oneself; subject oneself to: take a vow.
   c. To follow or adhere to (advice or a suggestion, for example).
   d. To accept or adopt as one’s own: take a stand on an issue; take an interest in local history.
   e. To regard or consider in a particular relation or from a particular viewpoint: We must take the bitter with the sweet. Take the matter as settled.
   f. To understand or interpret: May I take your smile as an indication of approval?
   g. To consider to be equal to; reckon: We take their number at 1,000.
   h. To perceive or feel; experience: I took a dislike to my neighbor’s intrusions.

10. a. To obtain from a source; derive or draw: This book takes its title from the Bible.
    b. To obtain, as through measurement or a specified procedure: took the patient’s temperature.
    c. To write or make a record of, especially in shorthand or cursive writing: take a letter; take notes.
    d. To create (an image, likeness, or representation), as by photography: took a picture of us.
    e. To include or distribute (a charge) in a financial record.

11. Informal To swindle, defraud, or cheat: You’ve really been taken.