DNA extraction from plants and algae don't use phenol. Why?
CTAB is for removing polyphenols and polysaccharides which are found in plant tissues. Animal cells/bacteria don't have these. You can do an additional phenol-chloroform extraction if you want.

See this protocol by Monsanto.


  
  Weigh out 6g of processed tissue into a 50ml conical tube appropriate for centrifugation. Note: For unprocessed tissue, weighing
  m ay occur prior to processing as long as entire processed sample is
  transferred to the conical tube. 
  For each 6g sample add 25ml of a solution consisting of 24.25ml, pre-warmed (55°C) CTAB extraction buffer, 0.5ml 2-mercaptoethanol
  (2-ME), and 0.25 ml of 10mg/ml proteinase K for a final concentration
  of 2% (2-ME) and 100µg/ml (proteinase K). 
  Incubate the tube for 60 minutes at 55°C. Cool the tube briefly on bench (10 minutes) 
  Add 20ml of phenol:chloroform:isoamyl alcohol (PCI, 25:24:1).  Cap the tube and mix vigorously by vortex or inversion. 
  Centrifuge for 10 minutes at 13,000×g and 20-25°C to separate the aqueous and organic phases. Transfer the upper aqueous phase to a
  clean 50ml conical tube. 
  Repeat extraction two times for a total of three extractions (steps 4-5).  
  Transfer upper aqueous phase to a new tube and add approximately 2/3 volume of -20°C isopropanol and gently invert the tube several
  times to mix. 
  To precipitate the DNA place the tubes at -20°C for at least 30 minutes and up to three days. 
  To pellet the DNA centrifuge the tubes at approximately 13,000×g for 20 minutes at 4°C. 
  Redissolve the pellet in 4 ml of TE pH 8.0. Transfer to a 13ml Sarstedt tube and add approximately 40µl of 10mg/ml RNase, then
  incubate at 37°C for 30 minutes. 
  To extract the DNA add 4ml of chloroform:isoamyl alcohol (CIA, 24:1).  Centrifuge for 10 minutes at approximately 13,000×g at room
  temperature.  Transfer the upper aqueous phase to a clean Sarstedt
  tube. 
  Repeat step 11 then add half volume of 7.5M ammonium acetate, gently mix by inversion/pipette and add 2 volumes of 100% ethanol. Mix
  by inversion/pipette and place at -20°C for 30 minutes to overnight. 
  Centrifuge at 13,000×g for 20 minutes at 4°C to pellet the DNA.